BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Bruno Amorim (Universidade do Minho) DTSTART:20200513T100000Z DTEND:20200513T110000Z DTSTAMP:20260422T225717Z UID:QM3/1 DESCRIPTION:Title: Stra in in two-dimensional materials\nby Bruno Amorim (Universidade do Minh o) as part of Quantum Matter meets Maths (IST\, Lisbon)\n\n\nAbstract\nGra phene is the prototypical two-dimensional material. One of main features o f two-dimensional materials is the ease with which their properties can be externally modified. Application of strain is one possible way. In this s eminar we will review the geometrical description of strains in crystallin e materials\, with a focus on graphene. Using this method\, we will study the form of the electron-lattice interaction. We will compare this model w ith the description of electrons in strained graphene in terms of a Dirac equation in curved space. An overview of anharmonic lattice effects in two -dimensional materials will also be made.\n LOCATION:https://researchseminars.org/talk/QM3/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Joe Huxford (Oxford University) DTSTART:20200520T100000Z DTEND:20200520T110000Z DTSTAMP:20260422T225717Z UID:QM3/2 DESCRIPTION:Title: Topo logical phases in 3+1D: the higher lattice gauge theory model and its exci tations\nby Joe Huxford (Oxford University) as part of Quantum Matter meets Maths (IST\, Lisbon)\n\n\nAbstract\nTopological phases in 3+1D are l ess well understood than\ntheir lower dimensional counterparts. A useful a pproach to the study\nof such phases is to look at toy models that we can solve exactly. In\nthis talk I will present new results for an existing mo del for certain\ntopological phases in 3+1D (the model was first presented in [1]).\nThis model is based on a generalisation of lattice gauge theory known\nas higher lattice gauge theory\, which treats parallel transport o f\nlines as well as points. I will first provide a brief introduction to\n higher lattice gauge theory and the Hamiltonian model constructed from\nit . Then we will look at the simple excitations (both point-like and\nloop-l ike) that are present in this model and how these excitations\ncan be cons tructed explicitly using so-called ribbon and membrane\noperators. Some of the quasi-particles are confined and we discuss how\nthis arises from a c ondensation-confinement transition. We will then\nlook at the (loop-)braid ing relations of the excitations and finish by\nexamining the conserved to pological charges realised by the Higher\nLattice Gauge Theory Model.
\n\n[1] A Bullivant\, M. Calcada et al.\, ``Topological phases from higher \ngauge symmetry in 3+1D"\, Phys. Rev. B 95\, 155118 (2017)\n LOCATION:https://researchseminars.org/talk/QM3/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Achilleas Lazarides (Loughborough University) DTSTART:20200527T100000Z DTEND:20200527T110000Z DTSTAMP:20260422T225717Z UID:QM3/3 DESCRIPTION:Title: Quan tum order at infinite temperature\, time crystals\, and dissipation\nb y Achilleas Lazarides (Loughborough University) as part of Quantum Matter meets Maths (IST\, Lisbon)\n\n\nAbstract\nDiscrete time crystals is the na me given to many-body systems displaying long-time dynamics that is sub-ha rmonic with respect to a driving frequency. While these were first discuss ed in closed quantum systems a few years ago\, recent work (partly motivat ed by experiments) has focussed on including non-unitary effects such as d ue to an external environment ("dissipation").\n\nIn this talk I will begi n by discussing general features of periodically-driven many-body systems\ , then concentrate on one of the unitary models for discrete time crystals . Time permitting\, I will finally I will discuss a general framework for subharmonic oscillations stabilised by dissipative dynamics.\n LOCATION:https://researchseminars.org/talk/QM3/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Johanna Erdmenger (University of Würzburg) DTSTART:20200603T100000Z DTEND:20200603T110000Z DTSTAMP:20260422T225717Z UID:QM3/4 DESCRIPTION:Title: Turb ulent hydrodynamics in strongly correlated Kagome metals\nby Johanna E rdmenger (University of Würzburg) as part of Quantum Matter meets Maths ( IST\, Lisbon)\n\n\nAbstract\nA current challenge in condensed matter physi cs is the realization of strongly correlated\, viscous electron fluids. Th ese fluids are not amenable to the perturbative methods of Fermi liquid th eory\, but can be described by holography\, that is\, by mapping them onto a weakly curved gravitational theory via gauge/gravity duality. The canon ical system considered for realizations has been graphene\, which possesse s Dirac dispersions at low energies as well as significant Coulomb interac tions between the electrons. In this work\, we show that Kagome systems wi th electron fillings adjusted to the Dirac nodes of their band structure p rovide a much more compelling platform for realizations of viscous electro n fluids\, including non-linear effects such as turbulence. In particular\ , we find that in stoichiometric Scandium (Sc) Herbertsmithite\, the fine- structure constant\, which measures the effective Coulomb interaction and hence reflects the strength of the correlations\, is enhanced by a factor of about 3.2 as compared to graphene\, due to orbital hybridization. We em ploy holography to estimate the ratio of the shear viscosity over the entr opy density in Sc-Herbertsmithite\, and find it about three times smaller than in graphene. These findings put\, for the first time\, the turbulent flow regime described by holography within the reach of experiments.\n LOCATION:https://researchseminars.org/talk/QM3/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Zlatko Papic (University of Leeds) DTSTART:20200610T100000Z DTEND:20200610T110000Z DTSTAMP:20260422T225717Z UID:QM3/5 DESCRIPTION:Title: Quan tum many-body scars: a new form of weak ergodicity breaking in constrained quantum systems\nby Zlatko Papic (University of Leeds) as part of Qua ntum Matter meets Maths (IST\, Lisbon)\n\n\nAbstract\nRecent experiments o n large chains of Rydberg atoms [1] have demonstrated the possibility of r ealising one-dimensional\, kinetically constrained quantum systems. It was found that such systems exhibit surprising signatures of non-ergodic dyna mics\, such as robust periodic revivals in global quenches from certain in itial states. This weak form of ergodicity breaking has been interpreted a s a manifestation of "quantum many-body scars" [2]\, i.e.\, the many-body analogue of unstable classical periodic orbits of a single particle in a c haotic stadium billiard. Scarred many-body eigenstates have been shown to exhibit a range of unusual properties which violate the Eigenstate Thermal isation Hypothesis\, such as equidistant energy separation\, anomalous exp ectation values of local observables and subthermal entanglement entropy. I will demonstrate that these properties can be understood using a tractab le model based on a single particle hopping on the Hilbert space graph\, w hich formally captures the idea that scarred eigenstates form a representa tion of a large spin that is embedded in a thermalising many-body system. I will show that this picture allows to construct a more general family o f scarred models where the fundamental degree of freedom is a quantum cloc k [3]. These results suggest that scarred many-body bands give rise to a n ew universality class of constrained quantum dynamics\, which opens up opp ortunities for creating and manipulating novel states with long-lived cohe rence in systems that are now amenable to experimental study.
\n\n[1] H . Bernien et al.\, Nature 551\, 579 (2017).
\n[2] C. J. Turner\, A. A. Michailidis\, D. A. Abanin\, M. Serbyn\, Z. Papic\, Nat. Phys. 14\, 745 (2 018).
\n[3] Kieran Bull\, Ivar Martin\, and Z. Papic\, Phys. Rev. Lett. 123\, 030601 (2019).\n LOCATION:https://researchseminars.org/talk/QM3/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Mário Silveirinha (Instituto Superior Técnico) DTSTART:20200624T100000Z DTEND:20200624T110000Z DTSTAMP:20260422T225717Z UID:QM3/6 DESCRIPTION:Title: Topo logical theory of non-Hermitian photonic systems\nby Mário Silveirinh a (Instituto Superior Técnico) as part of Quantum Matter meets Maths (IST \, Lisbon)\n\n\nAbstract\nRecently\, topological materials and topological effects have elicited a great interest in the photonics community [1]. W hile condensed-matter phenomena are traditionally described by Hermitian o perators\, the same is not true in the context of macroscopic electrodynam ics where a dissipative response is the rule\, not the exception. In this talk\, I will discuss how to determine the topological phases of dissipati ve (non-Hermitian) photonic structures from first principles using a gauge -independent Green function [2\, 3]. It is shown that analogous to the Her mitian case\, the Chern number can be expressed as an integral of the syst em Green function over a line parallel to the imaginary-frequency axis. Th e approach introduces in a natural way the "band-gaps" of non-Hermitian sy stems as the strips of the complex-frequency plane wherein the system Gree n function is analytical. I apply the developed theory to nonreciprocal el ectromagnetic continua and photonic crystals\, with lossy and or gainy ele ments. Furthermore\, I discuss the validity of the bulk-edge correspondenc e in the non-Hermitian case.\n\n[1] L. Lu\, J. D. Joannopoulos\, M. Solja čić\, "Topological photonics"\, Nat. Photonics\, 8\, 821\, (2014).\n\n[2 ] M. G. Silveirinha\, "Topological theory of non-Hermitian photonic system s"\, Phys. Rev. B\, 99\, 125155\, 2019.\n\n[3] F. R. Prudêncio\, M. G. Si lveirinha\, First Principles Calculation of Topological Invariants of non- Hermitian Photonic Crystals\, arXiv:2003.01539\n LOCATION:https://researchseminars.org/talk/QM3/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Manuel Asorey (University of Zaragoza) DTSTART:20200708T100000Z DTEND:20200708T110000Z DTSTAMP:20260422T225717Z UID:QM3/8 DESCRIPTION:Title: Bulk -Edge dualities in Topological Matter\nby Manuel Asorey (University of Zaragoza) as part of Quantum Matter meets Maths (IST\, Lisbon)\n\n\nAbstr act\nNovel bulk-edge dualities have recently emerged in topological materi als from the observation of some phenomenological correspondences. The sim ilarity of these dualities with string theory dualities is very appealing and has boosted a quite significant number of cross field studies.\nWe ana lyze the bulk-edge dualities in the integer quantum Hall effect\, where du e to the simpler nature of planar systems the duality can be analyzed by p owerful analytic techniques. The results show that the correspondence is l ess robust than expected. In particular\, it is highly dependent of the ty pe of boundary conditions of the topological material. We introduce a form al proof of the equivalence of bulk and edge approaches to the quantizatio n of Hall conductivity for metallic plates with local boundary conditions. However\, the proof does not work for non-local boundary conditions\, lik e the Atiyah-Patodi-Singer boundary conditions\, due to the appearance of gaps between the bulk and edge states.\n LOCATION:https://researchseminars.org/talk/QM3/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Giandomenico Palumbo (Université Libre de Bruxelles) DTSTART:20200713T160000Z DTEND:20200713T170000Z DTSTAMP:20260422T225717Z UID:QM3/9 DESCRIPTION:Title: Four -dimensional semimetals with tensor monopoles: from surface states to topo logical responses\nby Giandomenico Palumbo (Université Libre de Bruxe lles) as part of Quantum Matter meets Maths (IST\, Lisbon)\n\n\nAbstract\n Quantum anomalies offer a useful guide for the exploration of transport ph enomena in topological semimetals. A prominent example is provided by the chiral magnetic effect in three-dimensional Weyl semimetals\, which stems from the chiral anomaly. Here\, we reveal a distinct quantum effect\, coin ed "parity magnetic effect"\, which is induced by the parity anomaly in a four-dimensional topological semimetal. Upon preserving time-reversal symm etry\, the spectrum of our model is doubly degenerate and the nodal (Dirac ) points behave like Z2 monopoles. When time-reversal symmetry is broken\, while preserving the sublattice (chiral) symmetry\, our system supports s pin- 3/2 quasiparticles and the corresponding Dirac-like cones host tensor monopoles characterized by a Z number\, the Dixmier-Douady invariant. In both cases\, the semimetal exhibits topologically protected Fermi arcs on its boundary. Besides its theoretical implications in both condensed matte r and quantum field theory\, the peculiar 4D magnetic effect revealed by o ur model could be measured by simulating higher-dimensional semimetals in synthetic matter.\n LOCATION:https://researchseminars.org/talk/QM3/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Raffaele Resta (Instituto Officina dei Materiali\, CNR\, Trieste\, Italy) DTSTART:20200629T160000Z DTEND:20200629T170000Z DTSTAMP:20260422T225717Z UID:QM3/10 DESCRIPTION:Title: The insulating state of matter: a geometrical theory\nby Raffaele Resta ( Instituto Officina dei Materiali\, CNR\, Trieste\, Italy) as part of Quant um Matter meets Maths (IST\, Lisbon)\n\n\nAbstract\nThe insulating versus conducting behavior of condensed matter is commonly addressed\nin terms of electronic excitations and/or conductivity. At variance with such wisdom\ , W. Kohn hinted in 1964 that the insulating state of matter reflects a pe culiar organization of the electrons in their ground state\, and does not require an energy gap.\nKohn’s “theory of the insulating state” got a fresh restart in 1999\; at the root of these\ndevelopments is the modern theory of polarization\, developed in the early 1990s\, and\nbased on a g eometrical concept (Berry phase). Since insulators and metals polarize\nin a qualitatively different way\, quantum geometry also discriminates insul ators\nfrom conductors. A common geometrical “marker”\, based on the q uantum metric\,\ncaracterizes all insulators (band insulators\, Anderson i nsulators\, Mott insulators\,\nquantum Hall insulators. . . )\; such marke r diverges in conductors.\n LOCATION:https://researchseminars.org/talk/QM3/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Lucas Sá (Instituto Superior Técnico and CEFEMA) DTSTART:20200617T100000Z DTEND:20200617T110000Z DTSTAMP:20260422T225717Z UID:QM3/11 DESCRIPTION:Title: Ran dom matrix theory of dissipative quantum chaos\nby Lucas Sá (Institut o Superior Técnico and CEFEMA) as part of Quantum Matter meets Maths (IST \, Lisbon)\n\n\nAbstract\nDescribing complex interacting quantum systems i s a daunting task. One very fruitful approach to this problem\, developed for unitary dynamics\, is to represent the Hamiltonian of a system by a la rge random matrix. This eventually led to the development of the field of quantum chaos. Arguably\, one of its most spectacular achievements was the identification of universal signatures of chaos in quantum systems\, char acterizing the correlations of their energy levels. In this talk\, we will focus on the recent application of (non-Hermitian) random matrix theory t o open quantum systems\, where dissipation and decoherence coexist with un itary dynamics. First\, we will discuss a class of stochastic Lindbladians with random Hamiltonian and independent random dissipation channels (jump operators)\, as a model for the generator of complicated nonunitary dynam ics. We will then explain what difficulties arise when combining dissipati on with quantum chaos\, and how to overcome them. In particular\, we discu ss a new non-Hermitian random matrix ensemble with eigenvalues on the toru s and how it connects to our recent proposal of using complex spacing rati os as a signature of dissipative quantum chaos.\n LOCATION:https://researchseminars.org/talk/QM3/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Christophe Garban (Université Lyon 1) DTSTART:20200720T160000Z DTEND:20200720T170000Z DTSTAMP:20260422T225717Z UID:QM3/12 DESCRIPTION:Title: A n ew point of view on topological phase transitions\nby Christophe Garba n (Université Lyon 1) as part of Quantum Matter meets Maths (IST\, Lisbon )\n\n\nAbstract\nTopological phase transitions were discovered by Berezins kii-Kosterlitz-Thouless in the 70's. They describe intriguing phase transi tions for classical spins systems such as the plane rotator model (or $XY$ model). I will start by reviewing how this phase transition arises in cas es such as:\n\nthe $XY$ model (spins on $\\mathbb{Z}^2$ with values in the unit circle)\nthe integer-valued Gaussian Free Field (or $\\mathbb{Z}$-fe rromagnet)\nAbelian Yang-Mills on $\\mathbb{Z}^4$\nI will then connect top ological phase transitions to a statistical reconstruction problem concern ing the Gaussian Free Field and will show that the feasibility of the reco nstruction undergoes a KT transition.\n\nThis is a joint work with Avelio Sepúlveda (Lyon) and the talk will be based mostly on the preprint: https ://arxiv.org/abs/2002.12284\n LOCATION:https://researchseminars.org/talk/QM3/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Raquel Queiroz (Weizmann Institute of Science) DTSTART:20200727T160000Z DTEND:20200727T170000Z DTSTAMP:20260422T225717Z UID:QM3/13 DESCRIPTION:Title: Bou ndary Obstructed Topological Phases\nby Raquel Queiroz (Weizmann Insti tute of Science) as part of Quantum Matter meets Maths (IST\, Lisbon)\n\n\ nAbstract\nSymmetry protected topological (SPT) phases are gapped phases o f matter that cannot be deformed to a trivial phase without breaking the s ymmetry or closing the bulk gap. Here\, we introduce a new notion of a top ological obstruction that is not captured by bulk energy gap closings in p eriodic boundary conditions. More specifically\, given a symmetric boundar y termination we say two bulk Hamiltonians belong to distinct bound­ary o bstructed topological phases (BOTPs) if they can be deformed to each other on a system with periodic boundaries\, but cannot be deformed to each oth er in the open system without closing the gap at at least one high symmetr y surface. BOTPs are not topological phases of matter in the standard sens e since they are adiabat­ically deformable to each other on a torus but\, similar to SPTs\, they are associated with boundary signatures in open sy stems such as surface states or fractional corner charges. In contrast to SPTs\, these boundary signatures are not anomalous and can be removed by s ymmetrically adding lower dimensional SPTs on the boundary\, but they are stable as long as the spectral gap at high-symmetry edges/surfaces remains open. We show that the double-mirror quadrupole model of [Science\, 357(6 346)\, 2018] is a prototypical example of such phases\, and present a deta iled analysis of several aspects of boundary obstructions in this model. I n addition\, we intro­duce several three-dimensional models having bounda ry obstructions\, which are characterized either by surface states or frac tional corner charges. We also provide a general framework to study bounda ry obstructions in free-fermion systems in terms of Wannier band represent ations (WBR)\, an extension of the recently-developed band representation formalism to Wannier bands. WBRs capture the notion of topological obstruc tions in the Wannier bands which can then be used to study topological obs tructions in the boundary spectrum by means of the correspondence between the Wannier and boundary spectra. This establishes a form of bulk-boundary correspondence for BOTPs by relating the bulk band representation to the boundary topology.\n LOCATION:https://researchseminars.org/talk/QM3/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Vincenzo Alba (University of Amsterdam) DTSTART:20200914T160000Z DTEND:20200914T170000Z DTSTAMP:20260422T225717Z UID:QM3/14 DESCRIPTION:Title: Hyd rodynamic framework for out-of-equilibrium entangled many-body systems \nby Vincenzo Alba (University of Amsterdam) as part of Quantum Matter mee ts Maths (IST\, Lisbon)\n\n\nAbstract\nEntanglement and entropy are key co ncepts standing at the foundations of quantum and statistical mechanics\, respectively. In the last decade the study of quantum quenches revealed th at these two concepts are intricately intertwined. For integrable models\, novel hydrodynamic approaches based on a quasiparticle picture emerged as a new platform allowing for a quantitative understanding of quantum infor mation dynamics in quantum many-body systems. Remarkably\, this gives fres h insights on how thermodynamics emerges in isolated out-of-equilibrium qu antum systems.\n\nI will start by reviewing this new unifying framework. I will then discuss several applications to entanglement-related quantities \, such as entanglement entropies\, mutual information\, logarithmic negat ivity. I will also show how the framework allows to study the interplay be tween quantum information dynamics and transport of local conserved quanti ties. Finally\, I will derive some simple bounds on the quantum informatio n scrambling in out-of-equilibrium systems.\n LOCATION:https://researchseminars.org/talk/QM3/14/ END:VEVENT BEGIN:VEVENT SUMMARY:Svetlana Jitomirskaya (University of California\, Irvine) DTSTART:20200907T160000Z DTEND:20200907T170000Z DTSTAMP:20260422T225717Z UID:QM3/15 DESCRIPTION:Title: And erson localization and local eigenvalue statistics\nby Svetlana Jitomi rskaya (University of California\, Irvine) as part of Quantum Matter meets Maths (IST\, Lisbon)\n\n\nAbstract\nPoisson local statistics of eigenval ues is widely accepted as a necessary signature of Anderson localization\, but so far has been rigorously established only for random systems. We wi ll argue that this paradigm is wrong\, and the reality is a lot more compl ex and interesting\, by presenting both rigorous results for the Harper an d Maryland models and numerics for other quasiperiodic and similar models with localization. We will also discuss a conjecture on what the distribut ion is in the general ergodic situation.\n LOCATION:https://researchseminars.org/talk/QM3/15/ END:VEVENT BEGIN:VEVENT SUMMARY:Masud Haque (Maynooth University) DTSTART:20201012T160000Z DTEND:20201012T170000Z DTSTAMP:20260422T225717Z UID:QM3/16 DESCRIPTION:Title: Eig enstate Thermalization\, random matrices and (non)local operators in many- body systems\nby Masud Haque (Maynooth University) as part of Quantum Matter meets Maths (IST\, Lisbon)\n\n\nAbstract\nThe eigenstate thermaliza tion hypothesis (ETH) is a cornerstone in our understanding of quantum sta tistical mechanics. The extent to which ETH holds for nonlocal operators ( observables) is an open question. I will address this question using an an alogy with random matrix theory. The starting point will be the constructi on of extremely non-local operators\, which we call Behemoth operators. Th e Behemoths turn out to be building blocks for all physical operators. Thi s construction allow us to derive scalings for both local operators and di fferent kinds of nonlocal operators.\n LOCATION:https://researchseminars.org/talk/QM3/16/ END:VEVENT BEGIN:VEVENT SUMMARY:Gil Refael (Institute for Quantum Information and Matter) DTSTART:20200921T160000Z DTEND:20200921T170000Z DTSTAMP:20260422T225717Z UID:QM3/17 DESCRIPTION:Title: Flo quet higher-order topological insulators: principles and path towards real izations\nby Gil Refael (Institute for Quantum Information and Matter) as part of Quantum Matter meets Maths (IST\, Lisbon)\n\n\nAbstract\nThe c o-existence of spatial and non-spatial symmetries together with appropriat e commutation/anticommutation relations between them can give rise to stat ic higher-order topological phases\, which host gapless boundary modes of co-dimension higher than one. Alternatively\, space-time symmetries in a F loquet system can also lead to anomalous Floquet boundary modes of higher co-dimensions\, with different commutation/anticommutation relations with respect to non-spatial symmetries. In my talk I will review how these dyna mical analogs of the static HOTI's emerge\, and also show how a coherently excited phonon mode can be used to support non-trivial Floquet higher-ord er topological phases. If time allows\, I will also review recent work on Floquet engineering and band flattening of twisted-bilayer graphene.\n LOCATION:https://researchseminars.org/talk/QM3/17/ END:VEVENT BEGIN:VEVENT SUMMARY:Tom Claeys (Université Catholique de Louvain) DTSTART:20200928T160000Z DTEND:20200928T170000Z DTSTAMP:20260422T225717Z UID:QM3/18 DESCRIPTION:Title: Def ormed Airy kernel determinants: from KPZ tails to initial data for KdV \nby Tom Claeys (Université Catholique de Louvain) as part of Quantum Mat ter meets Maths (IST\, Lisbon)\n\n\nAbstract\nFredholm determinants associ ated to deformations of the Airy kernel are closely connected to the solut ion to the Kardar-Parisi-Zhang (KPZ) equation with narrow wedge initial da ta\, and they also appear as largest particle distribution in models of po sitive-temperature free fermions. I will explain how logarithmic derivativ es of the Fredholm determinants can be expressed in terms of a $2\\times 2 $ Riemann-Hilbert problem.\nThis Riemann-Hilbert representation can be use d to derive precise lower tail asymptotics for the solution of the KPZ equ ation with narrow wedge initial data\, refining recent results by Corwin a nd Ghosal\, and it reveals a remarkable connection with a family of unboun ded solutions to the Korteweg-de Vries (KdV) equation and with an integro- differential version of the Painlevé II equation.\n LOCATION:https://researchseminars.org/talk/QM3/18/ END:VEVENT BEGIN:VEVENT SUMMARY:Barry Simon (Caltech) DTSTART:20201019T120000Z DTEND:20201019T130000Z DTSTAMP:20260422T225717Z UID:QM3/19 DESCRIPTION:Title: Ber ry's Phase\, TKN$^2$ Integers and All That: My work on Topology in Condens ed Matter\nby Barry Simon (Caltech) as part of Quantum Matter meets Ma ths (IST\, Lisbon)\n\n\nAbstract\nI will give an overview of my work on to pological methods in condensed matter physics almost 40 years ago. Include will be Homotopy and TKN$^2$ integers\, holonomy and Berry's phase and qu arternions and Berry's phase for Fermions. If time allows\, I'll discuss s upersymmetry and pairs of projections.\n LOCATION:https://researchseminars.org/talk/QM3/19/ END:VEVENT BEGIN:VEVENT SUMMARY:Joseph Maciejko (University of Alberta) DTSTART:20201026T170000Z DTEND:20201026T180000Z DTSTAMP:20260422T225717Z UID:QM3/20 DESCRIPTION:Title: Hyp erbolic band theory\nby Joseph Maciejko (University of Alberta) as par t of Quantum Matter meets Maths (IST\, Lisbon)\n\n\nAbstract\nThe notions of Bloch wave\, crystal momentum\, and energy bands are commonly regarded as unique features of crystalline materials with commutative translation s ymmetries. Motivated by the recent realization of hyperbolic lattices in c ircuit QED\, I will present a hyperbolic generalization of Bloch theory\, based on ideas from Riemann surface theory and algebraic geometry. The the ory is formulated despite the non-Euclidean nature of the problem and conc omitant absence of commutative translation symmetries. The general theory will be illustrated by examples of explicit computations of hyperbolic Blo ch wavefunctions and bandstructures.\n LOCATION:https://researchseminars.org/talk/QM3/20/ END:VEVENT BEGIN:VEVENT SUMMARY:Benoît Douçot (LPTHE\, CNRS and Sorbonne Université\, Paris) DTSTART:20201109T160000Z DTEND:20201109T170000Z DTSTAMP:20260422T225717Z UID:QM3/21 DESCRIPTION:Title: Spi n textures in quantum Hall ferromagnets\nby Benoît Douçot (LPTHE\, C NRS and Sorbonne Université\, Paris) as part of Quantum Matter meets Math s (IST\, Lisbon)\n\n\nAbstract\nIn the presence of a strong magnetic field \, and for an integer filling of the Landau levels\, Coulomb interactions favor a ferromagnetic ground-state. It has been shown already twenty years ago\, both theoretically and experimentally\, that when extra charges are added or removed to such systems\, the ferromagnetic state becomes unstab le and is replaced by spin textures called Skyrmions. We have generalized this notion to an arbitrary number $N$ of internal states for the electron s\, which may correspond to the combination of spin\, valley\, or layer in dices. The first step is to associate a many electron wave-function\, proj ected on the lowest Landau level\, to any classical spin texture described by a smooth map from the plane to the projective space $\\mathbb{CP}^{N-1 }$. In the large magnetic field limit\, we assume that the spin texture is slowly varying on the scale of the magnetic length\, which allows us to e valuate the expectation value of the interaction Hamiltonian on these many electron quantum states. The first non trivial term in this semi-classica l expansion is the usual $\\mathbb{CP}^{N-1}$ non-linear sigma model\, whi ch is known to exhibit a remarkable degeneracy of the many electron states obtained from holomorphic textures. Surprisingly\, this degeneracy is not lifted by reintroducing quantum fluctuations. It is eventually lifted by the sub-leading term in the effective Hamiltonian\, which selects a hexago nal Skyrmion lattice and therefore breaks both translational and internal $SU(N)$ symmetries. I will show that these optimal classical textures can be interpreted in an appealing way using geometric quantization.\n LOCATION:https://researchseminars.org/talk/QM3/21/ END:VEVENT BEGIN:VEVENT SUMMARY:Jiannis K. Pachos (University of Leeds) DTSTART:20201116T170000Z DTEND:20201116T180000Z DTSTAMP:20260422T225717Z UID:QM3/22 DESCRIPTION:Title: Les s is more: effective description of topological spin liquids\nby Jiann is K. Pachos (University of Leeds) as part of Quantum Matter meets Maths ( IST\, Lisbon)\n\n\nAbstract\nIt is widely accepted that topological superc onductors can only have an effective interpretation in terms of curved geo metry rather than gauge fields due to their charge neutrality. This approa ch is commonly employed in order to investigate their properties\, such as the behaviour of their energy currents\, though we do not know how accura te it is. I will show that the low-energy properties of the Kitaev honeyco mb lattice model\, such as the shape of Majorana zero modes or the deforma tions of the correlation length\, are faithfully described in terms of Rie mann-Cartan geometry. Moreover\, I will present how effective axial gauge fields can couple to Majorana fermions\, thus giving a unified picture bet ween vortices and lattice dislocations that support Majorana zero modes.\n LOCATION:https://researchseminars.org/talk/QM3/22/ END:VEVENT BEGIN:VEVENT SUMMARY:Gourab Ray (University of Victoria) DTSTART:20201130T170000Z DTEND:20201130T180000Z DTSTAMP:20260422T225717Z UID:QM3/23 DESCRIPTION:Title: Uni versality of dimers via imaginary geometry\nby Gourab Ray (University of Victoria) as part of Quantum Matter meets Maths (IST\, Lisbon)\n\n\nAbs tract\nThe dimer model is a model of uniform perfect matching and is one o f the fundamental models of statistical physics. It has many deep and intr icate connections with various other models in this fiel\, namely the Isin g model and the six-vertex model.\n\nThis model has received a lot of atte ntion in the mathematics community in the past two decades. The primary re ason behind such popularity is that this model is integrable\, in particul ar\, the correlation functions can be represented exactly in a determinent al form. This gives rise to a rich interplay between algebra\, geometry\, probability and theoretical physics.\nFor graphs with very regular local s tructures\, exact computations of the correlation functions are possible b y Kasteleyn theory. R. Kenyon pioneered the development of the subject in this direction by proving that the fluctuations of the height function ass ociated to the dimer model on the square lattice converges to the Gaussian free field (a conformally invariant Gaussian field). However\, such compu tations seem only possible on graphs with special local structures\, while the dimer model is supposed to have GFF type fluctuations in a much more general setting.\n\nIn this talk\, I will give an overview of an ongoing p roject with N\, Berestycki (U. Vienna) and B. Laslier (Paris—Diderot 7) where we establish a form of universality about the GFF fluctuation of the dimer model. Our approach does not use Kasteleyn theory\, but uses a mapp ing known since Temperley—Fisher\, which maps the dimer model to uniform spanning trees. Remarkably\, as observed by Benjamini\, the “winding” of the branches of this spanning tree exactly measures the height functio n of the dimers. We combine this approach with the developing universal sc aling limit results of the uniform spanning trees\, revolutionized by Schr amm through the discovery of SLE. We show that the continuum ``winding” of these continuum limiting spanning trees converge to the GFF and harness from this the universality of the scaling limit. A key input in identifyi ng the limit is the so-called imaginary geometry developed by Miller and S heffield. In a more recent work\, we extend this universality partially to general Riemann surfaces as well.\n\nThis talk is based on the following preprints and some works in progress.\n\nhttps://projecteuclid.org/euclid. aop/1585123322
\nhttps://arxiv.org/abs/1610.07994
\nhttps://arxiv. org/abs/1908.00832\n LOCATION:https://researchseminars.org/talk/QM3/23/ END:VEVENT BEGIN:VEVENT SUMMARY:Enej Ilievski (University of Ljubljana) DTSTART:20201102T170000Z DTEND:20201102T180000Z DTSTAMP:20260422T225717Z UID:QM3/24 DESCRIPTION:Title: Sup eruniversality of superdiffusion\nby Enej Ilievski (University of Ljub ljana) as part of Quantum Matter meets Maths (IST\, Lisbon)\n\n\nAbstract\ nEmergence of anomalous transport laws in deterministic interacting many-b ody systems has become a subject of intense study in the past few years. O ne of the most prominent examples is the unexpected discovery of superdiff usive spin dynamics in the isotropic Heisenberg quantum spin chain with at half filling\, which falls into the universality class of the celebrated Kardar-Parisi-Zhang equation. In this talk\, we will theoretically justify why the observed superdiffusion of the Noether charges with anomalous dyn amical exponent $z=3/2$ is indeed superuniversal\, namely it is a feature of all integrable interacting lattice models or quantum field theories whi ch exhibit globally symmetry of simple Lie group $G$\, in thermal ensemble s that do not break $G$-invariance. The phenomenon can be attributed to th ermally dressed giant quasiparticles\, whose properties can be traced back to fusion relations amongst characters of quantum groups called Yangians. Giant quasiparticles can be identified with classical solitons\, i.e. sta ble nonlinear solutions to certain integrable PDE representing classical f erromagnet field theories on certain types of coset manifolds. We shall ex plain why these inherently semi-classical objects are in one-to-one corres pondence with the spectrum of Goldstone modes. If time permits\, we shall introduce another type of anomalous transport law called undular diffusion that generally occurs amongst the symmetry-broken Noether fields in $G$-i nvariant dynamical systems at finite charge densities.\n LOCATION:https://researchseminars.org/talk/QM3/24/ END:VEVENT BEGIN:VEVENT SUMMARY:Eslam Khalaf (Harvard University) DTSTART:20201123T170000Z DTEND:20201123T180000Z DTSTAMP:20260422T225717Z UID:QM3/25 DESCRIPTION:Title: Loc alization at the edge of a topological insulator: Interplay of disorder-in duced-localization and topological protection\nby Eslam Khalaf (Harvar d University) as part of Quantum Matter meets Maths (IST\, Lisbon)\n\n\nAb stract\nTransport in disordered one-dimensional wires is described by diff usion at short distances/times and by Anderson localization at long distan ces/times. I will investigate how this picture is altered in a disordered multi-channel wire where some of the channels are topologically protected. This scenario can be realized at the interface between two quantum Hall s ystems\, in a Weyl semimetal in a magnetic field or at the edge of a quant um spin Hall insulator. Technically\, the problem is described by a $0+1$- dimensional field theory in the form of a supersymmetric non-linear sigma model with a topological term. I will show how to solve this field theory exactly to obtain DC (static) transport quantities such as DC conductance and shot noise as well as dynamical responses such as diffusion probabilit y of return and correlations of local density of states. I will discuss se veral surprising findings of this exact solution. First\, I find that diso rder is much more effective in localizing the diffusive channels in the pr esence of topologically protected ones. This can be understood in terms of statistical level repulsion by mapping the problem to that of a random ma trix ensemble with zero eigenvalues. Second\, I find that localization cor rections dramatically alter the long time behavior of the return probabili ty in a system described by diffusion+drift equation at the classical leve l. Finally\, I find that in a disordered wire with topologically protected channels\, the wave functions display level attraction rather than level repulsion.\n LOCATION:https://researchseminars.org/talk/QM3/25/ END:VEVENT BEGIN:VEVENT SUMMARY:Lev Vidmar (Jozef Stefan Institute and University of Ljubljana) DTSTART:20201207T170000Z DTEND:20201207T180000Z DTSTAMP:20260422T225717Z UID:QM3/26 DESCRIPTION:Title: Ent anglement entropy in many-body eigenstates of local Hamiltonians\nby L ev Vidmar (Jozef Stefan Institute and University of Ljubljana) as part of Quantum Matter meets Maths (IST\, Lisbon)\n\n\nAbstract\nThe eigenstate en tanglement entropy is a powerful tool to distinguish integrable from gener ic quantum-chaotic Hamiltonians. In integrable models\, the average eigens tate entanglement entropy (over all Hamiltonian eigenstates) has a volume- law coefficient that generally depends on the subsystem fraction. In contr ast\, the volume-law coefficient is maximal (subsystem fraction independen t) in quantum-chaotic models. In the seminar I will present an overview of our current understanding of bipartite entanglement entropies in many-bod y quantum states above the ground states\, and contrast analytical predict ions with numerical results for eigenstates of physical Hamiltonians.\n LOCATION:https://researchseminars.org/talk/QM3/26/ END:VEVENT BEGIN:VEVENT SUMMARY:Takashi Oka (University of Tokyo) DTSTART:20201214T100000Z DTEND:20201214T110000Z DTSTAMP:20260422T225717Z UID:QM3/27 DESCRIPTION:Title: Flo quet Engineering of Quantum Materials\nby Takashi Oka (University of T okyo) as part of Quantum Matter meets Maths (IST\, Lisbon)\n\n\nAbstract\n

Periodic driving of quantum systems is attracting interest since we can use it to realize new states of matter with exotic properties. This conce pt\, known as Floquet engineering\, has been widely used in cold atoms [1] and recently in solid-state systems [2]. In this talk\, I plan to explain Floquet engineering basics using simple examples such a 2D and 3D Dirac e lectrons in circularly polarized laser fields [2]. Then\, to develop a mor e in-depth and intuitive understanding of Floquet states\, I will explain an example of a dynamical Landau quantization realized in oscillating magn etic fields.

\n\n\n

[1] A. Eckardt\, Rev. Mod. Phys. 89\, 011004 ( 2017).
\n[2] T. Oka\, S. Kitamura\, Annual Reviews of CMP\, 10:387 (2019).
\n[3] T. Oka\, L. Bucciantini\, Phys. Rev. B 94\, 155133 (2016).

\n LOCATION:https://researchseminars.org/talk/QM3/27/ END:VEVENT BEGIN:VEVENT SUMMARY:Michael Berry (University of Bristol) DTSTART:20210111T170000Z DTEND:20210111T180000Z DTSTAMP:20260422T225717Z UID:QM3/28 DESCRIPTION:Title: Geo metric phases and the separation of the world\nby Michael Berry (Unive rsity of Bristol) as part of Quantum Matter meets Maths (IST\, Lisbon)\n\n \nAbstract\nThe waves that describe systems in quantum physics can carry i nformation about how their environment has been altered\, for example by f orces acting on them. This effect is the geometric phase. It also occurs i n the optics of polarised light\, where it goes back to the 1830s\; and it gives insight into the spin-statistics relation for identical quantum par ticles. The underlying mathematics is geometric: the phenomenon of paralle l transport\, which also explains how falling cats land on their feet\, an d why parking a car in a narrow space is difficult. Incorporating the back -reaction of the geometric phase on the dynamics of the changing environme nt exposes the unsolved problem of how strictly a system can be separated from a slowly-varying environment\, and involves different mathematics: di vergent infinite series.\n LOCATION:https://researchseminars.org/talk/QM3/28/ END:VEVENT BEGIN:VEVENT SUMMARY:Sthitadhi Roy (University of Oxford) DTSTART:20210118T170000Z DTEND:20210118T180000Z DTSTAMP:20260422T225717Z UID:QM3/29 DESCRIPTION:Title: Man y-body localisation: a tale of correlations and classical percolation on F ock space\nby Sthitadhi Roy (University of Oxford) as part of Quantum Matter meets Maths (IST\, Lisbon)\n\n\nAbstract\nMany-body localised (MBL) phases of matter fall outside the conventional paradigm of equilibrium st atistical mechanics and thermodynamics. A natural question thus is\, what minimal and generic properties must random many-body Hamiltonians possess for a localised phase to be stable? In this talk\, I will address the ques tion by exploiting the exact mapping between a many-body Hamiltonian and a tight-binding problem on the Fock-space graph. In particular\, I will pre sent a theory for how the strong correlations in the effective Fock-space disorder play a central role in stabilising an MBL phase. The theory is r ooted in analytic but approximate calculations of the propagators on the F ock space. To shed further light on the underlying physics\, I will also i ntroduce and discuss a classical proxy for the MBL transition in the form of a percolation transition on the Fock space. Finally\, I will discuss a novel class of Anderson localisation problems on correlated trees\, to und erstand the effect of such disorder correlations in a more controlled sett ing.\n LOCATION:https://researchseminars.org/talk/QM3/29/ END:VEVENT BEGIN:VEVENT SUMMARY:Subir Sachdev (Harvard University) DTSTART:20210104T170000Z DTEND:20210104T180000Z DTSTAMP:20260422T225717Z UID:QM3/30 DESCRIPTION:Title: A s imple model of entangled qubits: how it describes superconductors and blac k holes\nby Subir Sachdev (Harvard University) as part of Quantum Matt er meets Maths (IST\, Lisbon)\n\n\nAbstract\nLong-range\, multi-particle q uantum entanglement plays a fundamental role in our understanding of many modern quantum materials\, including the copper-based high temperature sup erconductors. Hawking's quantum information puzzle in the quantum theory o f black holes also involves non-local entanglement. I will describe a simp le model of randomly entangled qubits which has shed light on these distin ct fields of physics.\n LOCATION:https://researchseminars.org/talk/QM3/30/ END:VEVENT BEGIN:VEVENT SUMMARY:Steve Simon (University of Oxford) DTSTART:20210125T170000Z DTEND:20210125T180000Z DTSTAMP:20260422T225717Z UID:QM3/31 DESCRIPTION:Title: Lat tice Geometry Dependence and Independence: Important Applications of a Si mple Law\nby Steve Simon (University of Oxford) as part of Quantum Mat ter meets Maths (IST\, Lisbon)\n\n\nAbstract\nThe ability to create and ma nipulate optical lattices for cold atoms\, with a view towards studying to pological matter\, has brought renewed focus to the physics of Bloch waves and the role of the lattice in governing their properties. We consider ge neric tight binding models where particle motion is described in terms of hopping amplitudes between orbitals. The physical attributes of the orbita ls\, including their locations in space\, are independent pieces of inform ation. We identify a notion of geometry-independence: any physical quantit y that depends only on the tight-binding parameters (and not on the explic it information about the orbital geometry) is said to be "geometry-indepen dent." Identification of geometry-dependent vs. independent quantities can be used as a novel principle for constraining a variety of results in bot h non-interacting and interacting systems. We show\, e.g.\, how Hall measu rements based on accelerated lattices or tilted potentials\, and those bas ed on applying a chemical potential imbalance between reservoirs\, give di fferent results due to the fact that one is geometry-dependent\, while the other is geometry-independent. Similar considerations apply for thermal H all responses in electronic\, cold atomic\, and spin systems.\n\n\nRef:\n\ nSteven H. Simon and Mark S. Rudner\, Phys. Rev. B 102\, 165148\, 2020.\n LOCATION:https://researchseminars.org/talk/QM3/31/ END:VEVENT BEGIN:VEVENT SUMMARY:Rémy Mosseri (LPTMC Sorbonne Université) DTSTART:20210208T100000Z DTEND:20210208T110000Z DTSTAMP:20260422T225717Z UID:QM3/32 DESCRIPTION:Title: Liq uid crystal director fields in three-dimensional non-Euclidean geometries< /a>\nby Rémy Mosseri (LPTMC Sorbonne Université) as part of Quantum Matt er meets Maths (IST\, Lisbon)\n\n\nAbstract\nThis work investigates nemati c liquid crystals in three-dimensional curved space\, and determines which director deformation modes are compatible with each possible type of non- Euclidean geometry. Previous work by Sethna et al. [1] showed that double twist is frustrated in flat space $\\mathbb{R}^3$\, but can fit perfectly in the hypersphere $\\mathbb{S}^3$. Here\, we extend that work to all four deformation modes (splay\, twist\, bend\, and biaxial splay) and all eigh t Thurston geometries [2]. Each pure mode of director deformation can fill space perfectly\, for at least one type of geometry. This analysis shows the ideal structure of each deformation mode in curved space\, which is fr ustrated by the requirements of flat space.\n\n[1] Sethna J P\,Wright D C and Mermin N D 1983 Phys. Rev. Lett. 51 467–70\n\n[2] J-F Sadoc\, R. Mos seri and J. Selinger\, New Journal of Physics 22 (2020) 093036\n LOCATION:https://researchseminars.org/talk/QM3/32/ END:VEVENT BEGIN:VEVENT SUMMARY:Maciej Koch-Janusz (University of Zurich) DTSTART:20210222T170000Z DTEND:20210222T180000Z DTSTAMP:20260422T225717Z UID:QM3/33 DESCRIPTION:Title: Sta tistical physics through the lens of real-space mutual information\nby Maciej Koch-Janusz (University of Zurich) as part of Quantum Matter meets Maths (IST\, Lisbon)\n\n\nAbstract\nIdentifying the relevant coarse-grain ed degrees of freedom in a complex physical system is a key stage in devel oping effective theories. The renormalization group (RG) provides a framew ork for this task\, but its practical execution in unfamiliar systems is f raught with ad hoc choices. Machine learning approaches\, on the other han d\, though promising\, often lack formal interpretability: it is unclear w hat relation\, if any\, the architecture- and training-dependent learned " relevant" features bear to standard objects of physical theory.\n\nI will present recent results addressing both issues. We develop a fast algorithm \, the RSMI-NE\, employing state-of-art results in machine-learning-based estimation of information-theoretic quantities to construct the optimal co arse-graining. We use it to develop a new approach to identifying the most relevant field theory operators describing a statistical system\, which w e validate on the example of interacting dimer model. I will also discuss formal results underlying the method: we establish equivalence between the information-theoretic notion of relevance defined in the Information Bott leneck (IB) formalism of compression theory\, and the field-theoretic rele vance of the RG. We show analytically that for statistical physical system s the "relevant" degrees of freedom found using IB compression indeed corr espond to operators with the lowest scaling dimensions\, providing a dicti onary connecting two distinct theoretical toolboxes.\n LOCATION:https://researchseminars.org/talk/QM3/33/ END:VEVENT BEGIN:VEVENT SUMMARY:Markus Heyl (Max-Planck Institute for the Physics of Complex Syste ms\, Dresden) DTSTART:20210322T170000Z DTEND:20210322T180000Z DTSTAMP:20260422T225717Z UID:QM3/34 DESCRIPTION:Title: Qua ntum many-body dynamics in two dimensions with artificial neural networks< /a>\nby Markus Heyl (Max-Planck Institute for the Physics of Complex Syste ms\, Dresden) as part of Quantum Matter meets Maths (IST\, Lisbon)\n\n\nAb stract\nIn the last two decades the field of nonequilibrium quantum many-b ody physics has seen a rapid development driven\, in particular\, by the r emarkable progress in quantum simulators\, which today provide access to d ynamics in quantum matter with an unprecedented control. However\, the eff icient numerical simulation of nonequilibrium real-time evolution in isola ted quantum matter still remains a key challenge for current computational methods especially beyond one spatial dimension. In this talk I will pres ent a versatile and efficient machine learning inspired approach. I will f irst introduce the general idea of encoding quantum many-body wave functio ns into artificial neural networks. I will then identify and resolve key c hallenges for the simulation of real-time evolution\, which previously imp osed significant limitations on the accurate description of large systems and long-time dynamics. As a concrete example\, I will consider the dynami cs of the paradigmatic two-dimensional transverse field Ising model\, wher e we observe collapse and revival oscillations of ferromagnetic order and demonstrate that the reached time scales are comparable to or exceed the c apabilities of state-of-the-art tensor network methods.\n LOCATION:https://researchseminars.org/talk/QM3/34/ END:VEVENT BEGIN:VEVENT SUMMARY:Anatoli Polkovnikov (Boston University) DTSTART:20210315T170000Z DTEND:20210315T180000Z DTSTAMP:20260422T225717Z UID:QM3/35 DESCRIPTION:Title: Eig enstate deformations as a sensitive probe of quantum chaos\nby Anatoli Polkovnikov (Boston University) as part of Quantum Matter meets Maths (IS T\, Lisbon)\n\n\nAbstract\nIn this talk I will discuss how one can detect quantum chaos in generic interacting models using adiabatic transformation s\, specifically the fidelity susceptibility. In particular\, I will show that it exhibits a very sharp crossover behavior from the algebraic to the exponential scaling form with the system size in the presence of a small integrability breaking parameter. This sensitivity allows one to identify tiny integrability breaking perturbations\, not detectable by conventional methods. I will also discuss that generically integrable and chaotic regi mes are separated by a universal regime of “maximal chaos” where the f idelity susceptibility saturates its upper bound and the system exhibits e xponentially slow\, glassy dynamics. I will illustrate how this probe work s using several examples of both clean and disordered systems and\, in par ticular\, will argue that numerical results indicate absence of a continuo us many-body localization transition in the thermodynamic limit.\n LOCATION:https://researchseminars.org/talk/QM3/35/ END:VEVENT BEGIN:VEVENT SUMMARY:David J. Luitz (Max Planck Institute for the Physics of Complex Sy stems\, Dresden) DTSTART:20210412T160000Z DTEND:20210412T170000Z DTSTAMP:20260422T225717Z UID:QM3/36 DESCRIPTION:Title: Hie rarchy of Relaxation Timescales in Local Random Liouvillians\nby David J. Luitz (Max Planck Institute for the Physics of Complex Systems\, Dresd en) as part of Quantum Matter meets Maths (IST\, Lisbon)\n\n\nAbstract\nTo characterize the generic behavior of open quantum many-body systems\, we consider random\, purely dissipative Liouvillians with a notion of localit y. We find that the positivity of the map implies a sharp separation of th e relaxation timescales according to the locality of observables. Specific ally\, we analyze a spin-$1/2$ system of size $\\ell$ with up to n-body L indblad operators\, which are n local in the complexity-theory sense. With out locality ($n=l$)\, the complex Liouvillian spectrum densely covers a “lemon”-shaped support\, in agreement with recent findings [S. Denisov et al.\, Phys. Rev. Lett. 123\, 140403 (2019)\, L. Sa et al.\, JPA 53\, 3 05303].\nHowever\, for local Liouvillians ($n < l$)\, we find that the spe ctrum is composed of several dense clusters with random matrix spacing sta tistics\, each featuring a lemon-shaped support wherein all eigenvectors c orrespond to $n$-body decay modes. This implies a hierarchy of relaxation timescales of n-body observables\, which we verify to be robust in the the rmodynamic limit. Our findings for n locality generalize immediately to th e case of spatial locality\, introducing further splitting of timescales d ue to the additional structure. \n\nTo test our theoretical prediction\, we perform experiments on the IBM quantum computing platform\, designing d ifferent "waiting circuits" to inject two body dissipative interactions by two qubit entangling gates. We find excellent agreement with our theory a nd observe the predicted hierarchy of timescales.\n\n\n\n\n\n[1] K. Wang\, F. Piazza\, D. J. Luitz ” Hierarchy of relaxation timescales in local r andom Liouvillians “ Phys. Rev. Lett. 124\, 100604 (2020)\n\n[2] O. E. S ommer\, F. Piazza\, and D. J. Luitz “Many-body Hierarchy of Dissipative Timescales in a Quantum Computer” arXiv:2011.08853\n LOCATION:https://researchseminars.org/talk/QM3/36/ END:VEVENT BEGIN:VEVENT SUMMARY:Xiao-Gang Wen (Massachusetts Institute of Technology) DTSTART:20210426T160000Z DTEND:20210426T170000Z DTSTAMP:20260422T225717Z UID:QM3/37 DESCRIPTION:Title: A h olographic view of symmetry -- symmetry as shadow of topological order \nby Xiao-Gang Wen (Massachusetts Institute of Technology) as part of Quan tum Matter meets Maths (IST\, Lisbon)\n\n\nAbstract\nRecently\, the notion of symmetry has been extended from 0-symmetry described by group to highe r symmetry described by higher group. In this talk\, we show that the noti on of symmetry can be generalized even further to "algebraic higher symmet ry". Then we will describe an even more general point of view of symmetry\ , which puts the (generalized) symmetry charges and topological excitation at equal footing: symmetry can be viewed as gravitational anomaly\, or sy mmetry can be viewed as shadow topological order in one higher dimension. This picture allows us to see many duality relations between seeming unrel ated symmetries.\n LOCATION:https://researchseminars.org/talk/QM3/37/ END:VEVENT BEGIN:VEVENT SUMMARY:Lea Santos (Yeshiva University) DTSTART:20210215T170000Z DTEND:20210215T180000Z DTSTAMP:20260422T225717Z UID:QM3/38 DESCRIPTION:Title: Ind icators of quantum chaos and the transition from few- to many-body systems \nby Lea Santos (Yeshiva University) as part of Quantum Matter meets M aths (IST\, Lisbon)\n\n\nAbstract\nQuantum chaos\, especially when caused by particle interactions\, is closely related with topics of high experime ntal and theoretical interest\, from the thermalization of isolated system s to the difficulties to reach a localized phase\, and the emergence of qu antum scars. In this talk\, various indicators of quantum chaos will be co mpared\, including level statistics\, structure of eigenstates\, matrix el ements of observables\, out-of-time ordered correlators\, and the correlat ion hole (ramp). These indicators are then employed to identify the minimu m number of interacting particles required for the onset of strong chaos i n quantum systems with short-range and also with long-range interactions.\ n\nRefs:\n\nhttps://arxiv.org/abs/2012.14436\nhttps://arxiv.org/abs/1802.0 8691\n LOCATION:https://researchseminars.org/talk/QM3/38/ END:VEVENT BEGIN:VEVENT SUMMARY:David Tong (University of Cambridge) DTSTART:20210517T160000Z DTEND:20210517T170000Z DTSTAMP:20260422T225717Z UID:QM3/39 DESCRIPTION:Title: How to Give Chiral Fermions a Mass\nby David Tong (University of Cambridg e) as part of Quantum Matter meets Maths (IST\, Lisbon)\n\n\nAbstract\nChi ral fermions have the property that their left-handed and right-handed com ponents transform differently under some symmetry. Folklore suggests that it is impossible to give such fermions a mass without breaking this symmet ry. I'll show\, through a number of examples\, why this folklore is wrong. In particular\, I'll show how one generation of fermions in the Standard Model can get a mass without the need for a Higgs boson that breaks electr oweak symmetry.\n LOCATION:https://researchseminars.org/talk/QM3/39/ END:VEVENT BEGIN:VEVENT SUMMARY:Alexander Altland (University of Cologne) DTSTART:20210329T160000Z DTEND:20210329T170000Z DTSTAMP:20260422T225717Z UID:QM3/40 DESCRIPTION:Title: Spe ctral density of weakly disordered Weyl semimetals\nby Alexander Altla nd (University of Cologne) as part of Quantum Matter meets Maths (IST\, Li sbon)\n\n\nAbstract\nWeyl semimetals contain an even number of singular po ints in their Brillouin zone around which the dispersion is linear and the density of states (DoS) vanishes. How does the density of states change i n the (inevitable) presence of impurities? This question has been the subj ect of an intensive and partially controversial discussion in the recent l iterature. In particular\, it has been suggested that below a critical dis order strength the DoS remains zero\, and that the system supports a phase transition separating an intrinsically clean from a disordered phase. In this talk\, I discuss this problem on the basis of several effective model s. All these support the integrity of the Weyl node and hence are compatib le with the above scenario. I will also comment on the (tricky) comparison to numerics and point out a puzzle whose solution invites mathematical re search.\n LOCATION:https://researchseminars.org/talk/QM3/40/ END:VEVENT BEGIN:VEVENT SUMMARY:Simon Becker (University of Cambridge) DTSTART:20210301T170000Z DTEND:20210301T180000Z DTSTAMP:20260422T225717Z UID:QM3/41 DESCRIPTION:Title: Mat hematics of magic angles for twisted bilayer graphene\nby Simon Becker (University of Cambridge) as part of Quantum Matter meets Maths (IST\, Li sbon)\n\n\nAbstract\nMagic angles are a hot topic in condensed matter phys ics: when two sheets of graphene are twisted by those angles the resulting material is superconducting. Please do not be scared by the physics thoug h: I will present a very simple operator whose spectral properties are tho ught to determine which angles are magical. It comes from a recent PR Lett er by Tarnopolsky–Kruchkov–Vishwanath. The mathematics behind this is an elementary blend of representation theory (of the Heisenberg group in c haracteristic three)\, Jacobi theta functions and spectral instability of non-self-adjoint operators (involving Hoermander’s bracket condition in a very simple setting). The results will be illustrated by colourful numer ics which suggest some open problems. This is joint work with M. Embree\, J. Wittsten\, and M. Zworski.\n LOCATION:https://researchseminars.org/talk/QM3/41/ END:VEVENT BEGIN:VEVENT SUMMARY:Hannah Price (Birmingham University) DTSTART:20210308T170000Z DTEND:20210308T180000Z DTSTAMP:20260422T225717Z UID:QM3/42 DESCRIPTION:Title: Exp loring 4D topological physics in the laboratory\nby Hannah Price (Birm ingham University) as part of Quantum Matter meets Maths (IST\, Lisbon)\n\ n\nAbstract\nSpatial dimensionality plays a key role in our understanding of topological physics\, with different topological invariants needed to c haracterise systems with different numbers of spatial dimensions. In a 2D quantum Hall system\, for example\, a robust quantisation of the Hall resp onse is related to the first Chern number: a 2D topological invariant of t he electronic energy bands. Generalising to more spatial dimensions\, it w as shown that a new type of quantum Hall effect could emerge in four dimen sions\, but where the quantised response was related to a four-dimensional topological invariant\, namely the second Chern number. While systems wit h four spatial dimensions may seem abstract\, recent developments in ultra cold atoms and photonics have opened the door to exploring such higher-dim ensional topological physics experimentally. In this talk\, I will introdu ce the theory of 4D topological phases of matter\, before discussing recen t experiments in cold atoms\, photonics and electrical circuits that have begun to probe aspects of this physics in the laboratory.\n LOCATION:https://researchseminars.org/talk/QM3/42/ END:VEVENT BEGIN:VEVENT SUMMARY:Karyn Le Hur (Centre de Physique Theorique\, École Polytechnique\ , CNRS) DTSTART:20210503T160000Z DTEND:20210503T170000Z DTSTAMP:20260422T225717Z UID:QM3/43 DESCRIPTION:Title: Geo metry\, Light Response and Quantum Transport in Topological States of Matt er\nby Karyn Le Hur (Centre de Physique Theorique\, École Polytechniq ue\, CNRS) as part of Quantum Matter meets Maths (IST\, Lisbon)\n\n\nAbstr act\nTopological states of matter are characterized by a gap in the bulk o f the system referring to an insulator or a superconductor and topological edge modes as well which find various applications in transport and spint ronics. The bulk-edge correspondence is associated to a topological number . The table of topological states include the quantum Hall effect and the quantum anomalous Hall effect\, topological insulators and topological sup erconductors in various dimensions and lattice geometries. Here\, we discu ss classes of states which can be understood from mapping onto a spin-1/2 particle in the reciprocal space of wave-vectors. We develop a geometrical approach on the associated Poincare-Bloch sphere\, developing smooth fiel ds\, which shows that the topology can be encoded from the poles only. We show applications for the light-matter coupling when coupling to circular polarizations and develop a relation with quantum transport and the quantu m Hall conductivity. The formalism allows to include interaction effects. We show our recent developments on a stochastic approach to englobe these interaction effects and discuss applications for the Mott transition of th e Haldane and Kane-Mele models. Then\, we develop a model of coupled spher es and show the possibility of fractional topological numbers as a result of interactions between spheres and entanglement allowing a superposition of two geometries\, one encircling a topological charge and one revealing a Bell or EPR pair. Then\, we show applications of the fractional topologi cal numbers C=1/2 in bilayer honeycomb models describing topological semi- metals characterized by a quantized Berry phase at one Dirac point.\n\n- J oel Hutchinson and Karyn Le Hur\, arXiv:2002.11823 (under review)\n\n- Phi lipp Klein\, Adolfo Grushin\, Karyn Le Hur\, Phys. Rev. B 103\, 035114 (20 21)\n LOCATION:https://researchseminars.org/talk/QM3/43/ END:VEVENT BEGIN:VEVENT SUMMARY:Igor Lesanovsky (Universität Tübingen) DTSTART:20210524T160000Z DTEND:20210524T170000Z DTSTAMP:20260422T225717Z UID:QM3/44 DESCRIPTION:Title: Neu ral network dynamics in open quantum many-body systems\nby Igor Lesano vsky (Universität Tübingen) as part of Quantum Matter meets Maths (IST\, Lisbon)\n\n\nAbstract\nOpen quantum systems composed of atoms interacting with light exhibit behaviour that is akin to that of associative memories [1]. This means that they possess stationary states that can be\ninterpre ted as stored memory patterns\, which are retrieved when the initial state is inside the basin of attraction of a given pattern [2]. The correspondi ng pattern retrieval dynamics can be observed in actual experimental setti ngs. In these experiments atoms are confined within an optical cavity whos e photons mediate long-range interactions [3]. Stored patterns are encoded in the atom-light coupling constants. This setting offers an interesting opportunity for studying quantum generalisations of associative memories a nd stored (quantum) patterns in this context [4]. Moreover\, it allows to systematically construct scenarios in which quantum effects might be benef icial\, e.g.\, for speeding up the pattern retrieval process [5]. I will t alk about recent research of my group on this subject\, which builds a bri dge between classic machine learning concepts\, such as the Hopfield Neura l Network\, and most recent experimental manifestations of synthetic quant um matter.\n\n\n\n[1] E. Fiorelli et al.\, Physical Review Letters 125\, 0 70604 (2020)\n\n[2] F. Carollo and I. Lesanovsky\, arXiv:2009.13932 (2020) \n\n[3] V.D. Vaidya et al.\, Physical Review X 8\, 011002 (2018)\n\n[4] P. Rotondo et al.\, Journal of Physics A 51\, 115301 (2018)\n\n[5] E. Fiorel li et al.\, Physical Review A 99\, 032126 (2019)\n LOCATION:https://researchseminars.org/talk/QM3/44/ END:VEVENT BEGIN:VEVENT SUMMARY:Rubem Mondaini (Beijing Computational Science Research Center) DTSTART:20210628T160000Z DTEND:20210628T170000Z DTSTAMP:20260422T225717Z UID:QM3/45 DESCRIPTION:Title: Qua ntum Critical Points and the Sign Problem\nby Rubem Mondaini (Beijing Computational Science Research Center) as part of Quantum Matter meets Mat hs (IST\, Lisbon)\n\n\nAbstract\nThe "sign problem" (SP) is the fundamenta l limitation to simulations of strongly correlated materials in condensed matter physics\, solving quantum chromodynamics at finite baryon density\, and computational studies of nuclear matter. It is often argued that the SP is not intrinsic to the physics of particular Hamiltonians\, since the details of how it onsets\, and its eventual occurrence\, can be altered by the choice of algorithm or many-particle basis. Despite that\, I plan to show in this talk that the SP in determinant quantum Monte Carlo (DQMC) is quantitatively linked to quantum critical behavior. This demonstration is done via simulations of a number of fundamental models of condensed matte r physics\, all of whose critical properties are relatively well understoo d.\n LOCATION:https://researchseminars.org/talk/QM3/45/ END:VEVENT BEGIN:VEVENT SUMMARY:Gunter M. Schütz (Institute of Biological Information Processing and Institute for Advanced Simulation) DTSTART:20210419T160000Z DTEND:20210419T170000Z DTSTAMP:20260422T225717Z UID:QM3/46 DESCRIPTION:Title: Spi n helix states in the dissipative Heisenberg quantum spin chain\nby Gu nter M. Schütz (Institute of Biological Information Processing and Instit ute for Advanced Simulation) as part of Quantum Matter meets Maths (IST\, Lisbon)\n\n\nAbstract\nWe demonstrate that the exact nonequilibrium steady state of the one-dimensional Heisenberg $XXZ$ spin chain driven by bounda ry Lindblad operators can be constructed explicitly with a matrix product ansatz for the nonequilibrium density matrix. For the isotropic Heisenberg chain\, polarized at the boundaries in different directions with a non-ze ro twist angle\, we calculate the exact magnetization profiles and magneti zation currents. The in-plane steady-state magnetization profiles are harm onic functions with a frequency proportional to the twist angle. In-plane steady-state magnetization currents are subdiffusive and vanish as the bou ndary coupling strength increases\, while the transverse current is diffus ive and saturates as the coupling strength becomes large. The anisotropic chain exhibits spin helix states at special values of the anisotropy where the transverse current is independent of system size\, even for non-integ rable higher-spin chains.\n LOCATION:https://researchseminars.org/talk/QM3/46/ END:VEVENT BEGIN:VEVENT SUMMARY:Michael Fleischhauer (Dept. of Physics & research center OPTIMAS\, Univ. of Kaiserslautern\, Germany) DTSTART:20210607T160000Z DTEND:20210607T170000Z DTSTAMP:20260422T225717Z UID:QM3/47 DESCRIPTION:Title: Top ology of mixed states\nby Michael Fleischhauer (Dept. of Physics & res earch center OPTIMAS\, Univ. of Kaiserslautern\, Germany) as part of Quant um Matter meets Maths (IST\, Lisbon)\n\n\nAbstract\nTopological states of matter have fascinated physicists since a long time. The notion of topolog y is however ususally associated with ground states of (many-body)-Hamilto nians\, which are pure. So what is left of it at finite temperatures and c an topological protection be extended to non-equilibrium steady states (NE SS) of open systems? Can suitable observables be constructed that preserve the integrity of topological invariants for mixed states and what are mea surable consequences of their existence? Can we classify the topology of f inite-temperature and NESS using generalized symmetries? Motivated by topo logical charge pumps\, first introduced by Thouless\, I will first discuss a topological invariant for systems that break time reversal symmetry bas ed on the many-body polarization\, called ensemble geometric phase (EGP) [ 1]. In contrast to charge transport\, the EGP can be used to probe topolog y in one dimensional non-interacting [2] and interacting [3]\, closed and open systems alike. Furthermore different from other constructions\, such as the Uhlmann phase\, it can be extended to two dimensions [4]. I will th en extend the definition to systems with time-reversal symmetry and finall y talk about measurable consequences of mixed-states topological invariant s.\n\n[1] C.E. Bardyn\, L. Wawer\, A. Altland\, M. Fleischhauer\, S.Diehl\ , (PRX 2018)\n\n[2] D. Linzner\, L. Wawer\, F. Grusdt\, M. Fleischhauer\, (PRB 2016)\n\n[3] R. Unanyan\, M. Kiefer-Emmanouilidis\, M. Fleischhauer\ , (PRL 2020)\n\n[4] L. Wawer\, M. Fleischhauer\, arxiv 2104.12115\n LOCATION:https://researchseminars.org/talk/QM3/47/ END:VEVENT BEGIN:VEVENT SUMMARY:Paul Melotti (Université Paris Saclay) DTSTART:20210510T160000Z DTEND:20210510T170000Z DTSTAMP:20260422T225717Z UID:QM3/48 DESCRIPTION:Title: The free-fermion eight-vertex model via dimers\nby Paul Melotti (Universi té Paris Saclay) as part of Quantum Matter meets Maths (IST\, Lisbon)\n\n \nAbstract\nThe eight-vertex model is an useful description that generaliz es several spin systems\, as well as the more common six-vertex model\, an d others. In a special "free-fermion" regime\, it is known since the work of Fan\, Lin\, Wu in the late 60s that the model can be mapped to non-bipa rtite dimers. However\, no general theory is known for dimers in the non-b ipartite case\, contrary to the extensive rigorous description of Gibbs me asures by Kenyon\, Okounkov\, Sheffield for bipartite dimers. In this talk I will show how to transform these non-bipartite dimers into bipartite on es\, on generic planar graphs. I will mention a few consequences: computat ion of long-range correlations\, criticality and critical exponents\, and their "exact" application to Z-invariant regimes on isoradial graphs.\n LOCATION:https://researchseminars.org/talk/QM3/48/ END:VEVENT BEGIN:VEVENT SUMMARY:Clement Delcamp (Max-Planck-Institute of Quantum Optics) DTSTART:20210614T160000Z DTEND:20210614T170000Z DTSTAMP:20260422T225717Z UID:QM3/49 DESCRIPTION:Title: On tensor network representations of the (3+1)d toric code\nby Clement De lcamp (Max-Planck-Institute of Quantum Optics) as part of Quantum Matter m eets Maths (IST\, Lisbon)\n\n\nAbstract\nTensor network states provide a c omprehensive framework for the analytic and numerical study of strongly co rrelated many-body systems. In recent years\, this framework has been succ essfully applied to topological phases of matter. In this talk\, I will pr esent two dual tensor network representations of the (3+1)d toric code gro und state subspace\, which are obtained by initially imposing either famil y of stabilizer constraints. I will discuss topological properties of the model from the point of view of these virtual symmetries\, demonstrate tha t one of these representations is stable to all local tensor perturbations ---including those that do not map to local operators on the physical Hilb ert space---and explain\, both from a physical and category theoretical vi ewpoint\, how the distinguishing properties of these representations are r elated to the phenomenon of bulk-boundary correspondence.\n LOCATION:https://researchseminars.org/talk/QM3/49/ END:VEVENT BEGIN:VEVENT SUMMARY:Ákos Nagy (University of California\, Santa Barbara) DTSTART:20210705T160000Z DTEND:20210705T170000Z DTSTAMP:20260422T225717Z UID:QM3/50 DESCRIPTION:Title: Con centrating Majorana fermions\nby Ákos Nagy (University of California\ , Santa Barbara) as part of Quantum Matter meets Maths (IST\, Lisbon)\n\n\ nAbstract\nI will begin by defining a canonical family of perturbations of the Dirac equation. These perturbations are complex anti-linear\, thus gr ound states only form a real vector space. A special case of this theory i s known as the Jackiw–Rossi theory\, which models surface excitations on the surface of a topological insulator placed in proximity to an s-wave s uperconductor. While the physics of the theory is relatively well-understo od\, the mathematical side has not been studied\, even on surfaces\, not t o mention its generalizations to higher dimensional and on nontrivial mani folds. I call these equations the ``generalized Jackiw–Rossi equations'' .\n\nAfter the definitions and connections to physics\, I will present my current work on the generalized Jackiw–Rossi equations. My main result i s a concentration phenomenon which proves the physical expectation that su ch Majorana fermions concentrate around the vortices of the superconductin g order parameter. Moreover\, I provide approximate solutions that are exp onentially sharp in the large coupling limit.\n\nIf time permits\, then I will show how these Majorana fermions define a bundle of projective spaces over the ``simple'' part of vortex moduli spaces. The holonomies of such bundles give rise to projective representations of (surface) braid groups\ , and thus\, speculatively\, can be of interest to quantum information the orists.\n LOCATION:https://researchseminars.org/talk/QM3/50/ END:VEVENT BEGIN:VEVENT SUMMARY:Sven Bachmann (University of British Columbia) DTSTART:20210719T160000Z DTEND:20210719T170000Z DTSTAMP:20260422T225717Z UID:QM3/51 DESCRIPTION:Title: Adi abatic quantum transport\nby Sven Bachmann (University of British Colu mbia) as part of Quantum Matter meets Maths (IST\, Lisbon)\n\n\nAbstract\n Recent years have seen much progress in the mathematical understanding of quantum charge transport under slow driving\, in the presence of strong in teractions between the charge carriers. I will give an overview of recent results\, starting with the adiabatic theorem in an interacting setting\, and continuing to topological transport where quantization can be shown to be valid beyond the linear response setting.\n LOCATION:https://researchseminars.org/talk/QM3/51/ END:VEVENT BEGIN:VEVENT SUMMARY:Dung Xuan Nguyen (Brown University) DTSTART:20211122T170000Z DTEND:20211122T180000Z DTSTAMP:20260422T225717Z UID:QM3/52 DESCRIPTION:Title: Mul tiple Gravitons and spectral sum rules in Fractional Quantum Hall systems< /a>\nby Dung Xuan Nguyen (Brown University) as part of Quantum Matter meet s Maths (IST\, Lisbon)\n\n\nAbstract\nIn this talk\, I will provide the hi storical review of magneto-roton excitation\, which is the gapped neutral excitation in the Lowest Landau Level. \nThe magneto-roton mode has spin-2 and can be considered as a massive graviton mode in 2+1D [1]. This spin-2 mode plays a central role in the physics of FQH. \nIn the current literat ure\, the spin-2 mode of Jain's sequences near filling fraction 1/2 can be thought of as the shear deformation of the composite fermion Fermi surfac e [2]. In this talk\, I will show that for Jain's sequences near filling f raction 1/4\, there will be an extra massive graviton mode [3]. The extra mode was proposed in our recent work on the Dirac composite fermion theory of general Jain's sequences in order to satisfy the Haldane bound of the static structure factor. The extra mode was confirmed numerically recently with the guidance of FQH sum rules [4]. I will briefly discuss our physic al interpretation of the new massive graviton mode. If time allows\, I wil l describe the experimental setup that can detect the graviton modes [5]. \n\nReferences:\n\n[1] Siavash Golkar\, Dung X. Nguyen and Dam T. Son JHE P 021\, 01 (2016) \n\n[2] DX Nguyen\, A Gromov\, DT Son\, Physical Revi ew B 97 (19)\, 195103 (2018)\n\n[3] DX Nguyen\, DT Son\, arXiv:2105.02092 (2021)\n\n[4] DX Nguyen\, Edward Rezayi\, Dam T. Son and Kun Yang To ap peared (Arxiv:2111.xxxxx)\n\n[5] DX Nguyen\, DT Son\, Phys. Rev. Research 3\, 023040 (2021)\n LOCATION:https://researchseminars.org/talk/QM3/52/ END:VEVENT BEGIN:VEVENT SUMMARY:Rosario Fazio (The Abdus Salam International Centre for Theoretica l Physics\, Trieste) DTSTART:20211018T160000Z DTEND:20211018T170000Z DTSTAMP:20260422T225717Z UID:QM3/53 DESCRIPTION:Title: Qua ntum time crystals\nby Rosario Fazio (The Abdus Salam International Ce ntre for Theoretical Physics\, Trieste) as part of Quantum Matter meets Ma ths (IST\, Lisbon)\n\n\nAbstract\nLandau's idea of classifying phases of m atter in terms of symmetry breaking is a cornerstone of modern physics. In his pioneering work Wilczek argued that an autonomous system can break t ime translation symmetry\, thus realising what he named as time crystals. Their existence has been confirmed very recently in a number of experiment s. I will briefly review the field focusing in particular on the so called Floquet time-crystals (arising in many-body systems that are periodically driven) and on time-crystalline behaviour in quantum open systems. For th is last case\, I will make connections to quantum synchronisation.\n LOCATION:https://researchseminars.org/talk/QM3/53/ END:VEVENT BEGIN:VEVENT SUMMARY:Karol Życzkowski (Jagiellonian University Cracow\, Poland\; Cente r for Theoretical Physics\, PAS\, Warsaw) DTSTART:20211129T170000Z DTEND:20211129T180000Z DTSTAMP:20260422T225717Z UID:QM3/55 DESCRIPTION:Title: Mul ti-unitary matrices and their quantum applications\nby Karol Życzkows ki (Jagiellonian University Cracow\, Poland\; Center for Theoretical Physi cs\, PAS\, Warsaw) as part of Quantum Matter meets Maths (IST\, Lisbon)\n\ n\nAbstract\nIn the space of bipartite unitary gates one distinguishes the set of local gates\, formed by a tensor product\, $U=V_A \\otimes V_B$. A nother distinguished set contains gates of extremal non-locality\, which m aximize the entropy of entanglement defined by the operator Schmidt decomp osition of a unitary gate $U$. If the reshuffled matrix\, $U^R$\, is also unitary the matrix $U$ belongs to this class and is called dual unitary. T he matrix $S$ corresponding to the SWAP operation is strongly non-local an d dual unitary\, but it does not change entanglement of any state it acts on. To describe creation of entanglement in the system one defines entangl ing power of a gate. Its absolute maximum is achieved for any dual unitary gate $U$\, such that its partial transpose $U^{\\Gamma}$ is also unitary. These gates\, called two-unitary\, do not exist for dimension $d=2^2$\, b ut exist for $d=3^2$. We present an analytical construction of such a gate U of order $d=6^2=36$\, which leads to a solution of the quantum version of the famous problem of $36$ officers of Euler [1]. It implies a pair of quantum orthogonal Latin squares of order six and an Absolutely Maximally Entangled (AME) state of four subsystems with six levels each. It enables us to construct a quhex pure nonadditive quantum error detection code usef ul to encode a 6-level state into a triple of such states. Using such a st ate one can teleport any unknown\, two-dice quantum state\, from any pair of two subsystems to the lab possessing the two other dice forming the fou r-dice system. Our result imples that $2$-unitary gates exist for any squa red dimension $d=N^2$ with $N\\ge 3$. A matrix $U$ of order $d=N^k$ is cal led k-unitary or multiunitary if it remains unitary after any of possible (2k choose k) reordering of the matrix. Any such a matrix leads to an AME state of $2k$ subsystems of size $N$. A simple example of a $3$-unitary ma trix $U$ of order $2^3=8$ corresponds to an AME(6\,2) state of six qubits. \n\nReferences:\n\n[1] S.A Rather\, A.Burchardt\, W. Bruzda\, G. Rajchel-M ieldzioć\, A. Lakshminarayan and K. Życzkowski\, Thirty-six entangled of ficers of Euler\, preprint arXiv:2104.05122\n LOCATION:https://researchseminars.org/talk/QM3/55/ END:VEVENT BEGIN:VEVENT SUMMARY:Cristiano Ciuti (Université de Paris\, CNRS\, Laboratoire Matéri aux et Phénomènes Quantiques\, France) DTSTART:20211220T170000Z DTEND:20211220T180000Z DTSTAMP:20260422T225717Z UID:QM3/56 DESCRIPTION:Title: Man ipulating matter with vacuum fields: cavity-mediated transport in quantum Hall systems\nby Cristiano Ciuti (Université de Paris\, CNRS\, Labora toire Matériaux et Phénomènes Quantiques\, France) as part of Quantum M atter meets Maths (IST\, Lisbon)\n\n\nAbstract\nThe manipulation of matter by giant vacuum fields in electromagnetic resonators is an emergent topic in physics and chemistry [1]. In this seminar\, after a general introduct ion\, we will see how the cavity vacuum fluctuations can dramatically affe ct the physics of disordered quantum Hall systems. In particular\, we will show how\, in the presence of electronic disorder\, the cavity can mediat e long-range electron hopping via the exchange of virtual photons\, involv ing both edge and bulk states [2]. Such an effect can produce a breakdown of the topological protection of the integer quantum Hall effect as demons trated in recent transport experiments [3]. Future perspectives will be di scussed.\n\n[1] F. J. Garcia-Vidal\, C. Ciuti\, T. W. Ebbesen\, Manipulati ng matter by strong coupling to vacuum fields\, Science 373\,178 (2021).\n \n[2] C. Ciuti\, Cavity-mediated electron hopping in disordered quantum Ha ll systems\, Phys. Rev. B 104\, 155307 (2021).\n\n[3] F. Appugliese\, J. E nkner\, G. L. Paravicini-Bagliani\, M. Beck\, C. Reichl\, W. Wegscheider\, G. Scalari\, C. Ciuti\, J. Faist\, Breakdown of the topological protectio n by cavity vacuum fields in the integer quantum Hall effect\, preprint ar Xiv:2107.14145 (2021)\, to appear in\nScience.\n LOCATION:https://researchseminars.org/talk/QM3/56/ END:VEVENT BEGIN:VEVENT SUMMARY:Omri Golan (QEDMA Quantum Computing\, Israel) DTSTART:20211115T170000Z DTEND:20211115T180000Z DTSTAMP:20260422T225717Z UID:QM3/57 DESCRIPTION:Title: Geo metric complexity in quantum matter: intrinsic sign problems in topologica l phases\nby Omri Golan (QEDMA Quantum Computing\, Israel) as part of Quantum Matter meets Maths (IST\, Lisbon)\n\n\nAbstract\nThe infamous sign problem leads to an exponential complexity in Monte Carlo simulations of generic many-body quantum systems. Nevertheless\, many phases of matter ar e known to admit a sign-problem-free representative\, allowing efficient s imulations on classical computers. Motivated by long standing open problem s in many-body physics\, as well as fundamental questions in quantum compl exity\, the possibility of intrinsic sign problems\, where a phase of matt er admits no sign-problem-free representative\, was recently raised but re mains largely unexplored. I will describe results establishing the existen ce\, and the geometric origin\, of intrinsic sign problems in a broad clas s of topological phases in 2+1 dimensions. Within this class\, these resul ts exclude the possibility of 'stoquastic' Hamiltonians for bosons\, and o f sign-problem-free determinantal Monte Carlo algorithms for fermions. The talk is based on Phys. Rev. Research 2\, 043032 and 033515.\n LOCATION:https://researchseminars.org/talk/QM3/57/ END:VEVENT BEGIN:VEVENT SUMMARY:Manfred Salmhofer (University of Heidelberg) DTSTART:20211025T160000Z DTEND:20211025T170000Z DTSTAMP:20260422T225717Z UID:QM3/58 DESCRIPTION:Title: Ren ormalization in condensed matter: Fermionic systems – from mathematics t o materials\nby Manfred Salmhofer (University of Heidelberg) as part o f Quantum Matter meets Maths (IST\, Lisbon)\n\n\nAbstract\nI review the ro le of renormalization theory in many-fermion systems\, both from the point of view of mathematical physics and that of applications to models of cor related electrons in solids. The Wilsonian renormalization group method al lows for an unbiased analysis of competing ordering tendencies\, such as m agnetism and superconductivity in effectively two-dimensional systems. As an example\, I will consider ferromagnetism and superconductivity in the H ubbard model at Van Hove filling.\n LOCATION:https://researchseminars.org/talk/QM3/58/ END:VEVENT BEGIN:VEVENT SUMMARY:Predrag Cvitanović (Georgia Tech) DTSTART:20211206T170000Z DTEND:20211206T180000Z DTSTAMP:20260422T225717Z UID:QM3/59 DESCRIPTION:Title: Her ding Cats: A Chaotic Field Theory\nby Predrag Cvitanović (Georgia Tec h) as part of Quantum Matter meets Maths (IST\, Lisbon)\n\n\nAbstract\nSup pose you find yourself face-to-face with Young-Mills or Navier-Stokes or a nonlinear PDE or a funky metamaterial or a cloudy day. And you ask yourse lf\, is this thing "turbulent" What does that even mean?\n\nIf you were ha d a serious course on 'chaos'\, as Professor Ribeiro had\, you must have l earned about the coin toss (Bernoulli map). I'll walk you through this bas ic example of deterministic chaos\, than through the 'kicked rotor'\, a ne at physical system that is chaotic\, and then put infinity of these togeth er to explain what `chaos' or `turbulence' looks like in the spacetime.\n\ nWhat emerges is a spacetime which is very much like a big spring mattress that obeys the familiar continuum versions of a harmonic oscillator\, the Helmholtz and Poisson equations\, but instead of being "springy"\, this m etamaterial has an unstable rotor at every lattice site\, that gives\, rat her than pushes back. We call this simplest of all chaotic field theories the `spatiotemporal cat'. There is a QM^3 version\, ask Boris Gutkin or To maž Prosen to tell\nyou about it.\n\nIn the spatiotemporal formulation of turbulence there is no evolution in time\, there are only a repertoires o f admissible spatiotemporal patterns. In other words: throw away your inte grators\, and look for guidance in clouds' repeating patterns.\n\nThat's ` turbulence'. $\\href{https://www.youtube.com/watch?v=_JZom_gVfuw}{\\text{A nd if you don't know\, now you know.}}$\n\n----------------------------\n\ nNo actual cats\, graduate or undergraduate\, have shown interest in\, or were harmed during this research.\n LOCATION:https://researchseminars.org/talk/QM3/59/ END:VEVENT BEGIN:VEVENT SUMMARY:Anton Kapustin (Caltech) DTSTART:20211213T170000Z DTEND:20211213T180000Z DTSTAMP:20260422T225717Z UID:QM3/60 DESCRIPTION:Title: Hig her Berry classes for many-body quantum lattice systems\nby Anton Kapu stin (Caltech) as part of Quantum Matter meets Maths (IST\, Lisbon)\n\n\nA bstract\nM. Berry showed how to attach a line bundle and a connection on i t to a family of quantum Hamiltonians with a non-degenerate ground state\, under the assumption that the Hilbert space is finite-dimensional. The fi rst Chern class of this line bundle is a topological invariant of the fami ly. It is far from obvious if this construction can be generalized to qua ntum many-body Hamiltonians. Indeed\, naive generalizations fail because g round states of different Hamiltonians typically correspond to inequivalen t representations of the algebra of observables. Nevertheless\, it is poss ible to construct such invariants by making use of a certain differential graded Lie algebra (DGLA) attached to a quantum lattice system. For exampl e\, it turns out that to any family of gapped Hamiltonians on a 1d lattice one can attach a “quantized” degree-3 cohomology class on the paramet er space. In this talk I will outline a construction of this DGLA as well as the construction of higher Berry classes. The talk is based on a work i n progress with Nikita Sopenko.\n LOCATION:https://researchseminars.org/talk/QM3/60/ END:VEVENT BEGIN:VEVENT SUMMARY:Dieter Mitsche (Université Jean Monnet\, France) DTSTART:20230220T140000Z DTEND:20230220T150000Z DTSTAMP:20260422T225717Z UID:QM3/61 DESCRIPTION:Title: Tai l bounds for detection times in dynamic hyperbolic graphs\nby Dieter M itsche (Université Jean Monnet\, France) as part of Quantum Matter meets Maths (IST\, Lisbon)\n\n\nAbstract\nMotivated by Krioukov et al's model of random hyperbolic graphs for real-world networks\, and inspired by the an alysis of a dynamic model of graphs in Euclidean space by Peres et al.\, w e introduce a dynamic model of hyperbolic graphs in which vertices are all owed to move according to a Brownian motion maintaining the distribution o f vertices in hyperbolic space invariant. For different parameters of the speed of angular and radial motion\, we analyze tail bounds for detection times of a fixed target and obtain a complete picture\, for very different regimes\, of how and when the target is detected: as a function of the ti me passed\, we characterize the subset of the hyperbolic space where parti cles typically detecting the target are initially located. We overcome sev eral substantial technical difficulties not present in Euclidean space\, a nd provide a complete picture on tail bounds. On the way\, we obtain also new results for the time more general continuous processes with drift and reflecting barrier spent in certain regions\, and we also obtain improved bounds for independent sums of Pareto random variables.\n\nJoint work with Marcos Kiwi and Amitai Linker.\n LOCATION:https://researchseminars.org/talk/QM3/61/ END:VEVENT END:VCALENDAR