\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;VALUE=DATE-TIME:20200527T100000Z DTEND;VALUE=DATE-TIME:20200527T110000Z DTSTAMP;VALUE=DATE-TIME:20240222T185910Z 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;VALUE=DATE-TIME:20200603T100000Z DTEND;VALUE=DATE-TIME:20200603T110000Z DTSTAMP;VALUE=DATE-TIME:20240222T185910Z 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;VALUE=DATE-TIME:20200610T100000Z DTEND;VALUE=DATE-TIME:20200610T110000Z DTSTAMP;VALUE=DATE-TIME:20240222T185910Z 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;VALUE=DATE-TIME:20200624T100000Z DTEND;VALUE=DATE-TIME:20200624T110000Z DTSTAMP;VALUE=DATE-TIME:20240222T185910Z 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;VALUE=DATE-TIME:20200708T100000Z DTEND;VALUE=DATE-TIME:20200708T110000Z DTSTAMP;VALUE=DATE-TIME:20240222T185910Z 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;VALUE=DATE-TIME:20200713T160000Z DTEND;VALUE=DATE-TIME:20200713T170000Z DTSTAMP;VALUE=DATE-TIME:20240222T185910Z 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;VALUE=DATE-TIME:20200629T160000Z DTEND;VALUE=DATE-TIME:20200629T170000Z DTSTAMP;VALUE=DATE-TIME:20240222T185910Z 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;VALUE=DATE-TIME:20200617T100000Z DTEND;VALUE=DATE-TIME:20200617T110000Z DTSTAMP;VALUE=DATE-TIME:20240222T185910Z 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;VALUE=DATE-TIME:20200720T160000Z DTEND;VALUE=DATE-TIME:20200720T170000Z DTSTAMP;VALUE=DATE-TIME:20240222T185910Z 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;VALUE=DATE-TIME:20200727T160000Z DTEND;VALUE=DATE-TIME:20200727T170000Z DTSTAMP;VALUE=DATE-TIME:20240222T185910Z 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;VALUE=DATE-TIME:20200914T160000Z DTEND;VALUE=DATE-TIME:20200914T170000Z DTSTAMP;VALUE=DATE-TIME:20240222T185910Z 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;VALUE=DATE-TIME:20200907T160000Z DTEND;VALUE=DATE-TIME:20200907T170000Z DTSTAMP;VALUE=DATE-TIME:20240222T185910Z 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;VALUE=DATE-TIME:20201012T160000Z DTEND;VALUE=DATE-TIME:20201012T170000Z DTSTAMP;VALUE=DATE-TIME:20240222T185910Z 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;VALUE=DATE-TIME:20200921T160000Z DTEND;VALUE=DATE-TIME:20200921T170000Z DTSTAMP;VALUE=DATE-TIME:20240222T185910Z 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;VALUE=DATE-TIME:20200928T160000Z DTEND;VALUE=DATE-TIME:20200928T170000Z DTSTAMP;VALUE=DATE-TIME:20240222T185910Z 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;VALUE=DATE-TIME:20201019T120000Z DTEND;VALUE=DATE-TIME:20201019T130000Z DTSTAMP;VALUE=DATE-TIME:20240222T185910Z 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;VALUE=DATE-TIME:20201026T170000Z DTEND;VALUE=DATE-TIME:20201026T180000Z DTSTAMP;VALUE=DATE-TIME:20240222T185910Z 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;VALUE=DATE-TIME:20201109T160000Z DTEND;VALUE=DATE-TIME:20201109T170000Z DTSTAMP;VALUE=DATE-TIME:20240222T185910Z 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;VALUE=DATE-TIME:20201116T170000Z DTEND;VALUE=DATE-TIME:20201116T180000Z DTSTAMP;VALUE=DATE-TIME:20240222T185910Z 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;VALUE=DATE-TIME:20201130T170000Z DTEND;VALUE=DATE-TIME:20201130T180000Z DTSTAMP;VALUE=DATE-TIME:20240222T185910Z 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;VALUE=DATE-TIME:20201102T170000Z DTEND;VALUE=DATE-TIME:20201102T180000Z DTSTAMP;VALUE=DATE-TIME:20240222T185910Z 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;VALUE=DATE-TIME:20201123T170000Z DTEND;VALUE=DATE-TIME:20201123T180000Z DTSTAMP;VALUE=DATE-TIME:20240222T185910Z 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;VALUE=DATE-TIME:20201207T170000Z DTEND;VALUE=DATE-TIME:20201207T180000Z DTSTAMP;VALUE=DATE-TIME:20240222T185910Z 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;VALUE=DATE-TIME:20201214T100000Z DTEND;VALUE=DATE-TIME:20201214T110000Z DTSTAMP;VALUE=DATE-TIME:20240222T185910Z 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).