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SUMMARY:Amanda Young (Techincal University of Munich)
DTSTART;VALUE=DATE-TIME:20211011T160500Z
DTEND;VALUE=DATE-TIME:20211011T165000Z
DTSTAMP;VALUE=DATE-TIME:20220528T202146Z
UID:BIRS-21w5502/1
DESCRIPTION:Title: A bulk gap in the presence of edge states for a Haldane pseudopotenti
al\nby Amanda Young (Techincal University of Munich) as part of BIRS w
orkshop: Topology and Entanglement in Many-Body Systems\n\n\nAbstract\nIn
this talk\, we discuss a recent result on a bulk gap for a truncated Halda
ne pseudopotential with maximal half filling\, which describes a strongly
correlated system of spinless bosons in a cylinder geometry. For this Hami
ltonian with either open or periodic boundary conditions\, we prove a spec
tral gap above the highly degenerate ground-state space which is uniform i
n the volume and particle number. Our proofs rely on identifying invariant
subspaces to which we apply gap-estimate methods previously developed onl
y for quantum spin Hamiltonians. In the case of open boundary conditions\,
the lower bound on the spectral gap accurately reflects the presence of e
dge states\, which do not persist into the bulk. Customizing the gap techn
ique to the invariant subspace\, we avoid the edge states and establish a
more precise estimate on the bulk gap in the case of periodic boundary con
ditions. The same approach can also be applied to prove a bulk gap for the
analogously truncated 1/3-filled Haldane pseudopotential for the fraction
al quantum Hall effect.\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5502/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anurag Anshu (UC Berkeley)
DTSTART;VALUE=DATE-TIME:20211011T173000Z
DTEND;VALUE=DATE-TIME:20211011T181500Z
DTSTAMP;VALUE=DATE-TIME:20220528T202146Z
UID:BIRS-21w5502/2
DESCRIPTION:Title: An area law for ground states of 2D frustration-free spin systems
\nby Anurag Anshu (UC Berkeley) as part of BIRS workshop: Topology and Ent
anglement in Many-Body Systems\n\n\nAbstract\nWe will discuss an area law
for ground states of locally gapped frustration-free 2D lattice spin syste
ms. We first generalize the optimal approximation of the boolean AND funct
ion to a non-commuting setting\, showing that the ground state projector o
f a locally gapped frustration-free 1D spin system can be optimally approx
imated in a similar manner. For 2D spin systems we then construct an appro
ximate ground state projector (AGSP) that employs the optimal 1D approxima
tion along the boundary of the bipartition of interest. If time permits\,
we will also discuss the challenges in extending the proof to 3D systems.
Joint work with Itai Arad and David Gosset (https://arxiv.org/abs/2103.024
92).\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5502/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yoshiko Ogata (The University of Tokyo)
DTSTART;VALUE=DATE-TIME:20211012T233000Z
DTEND;VALUE=DATE-TIME:20211013T001500Z
DTSTAMP;VALUE=DATE-TIME:20220528T202146Z
UID:BIRS-21w5502/3
DESCRIPTION:Title: Classification of SPT phases\nby Yoshiko Ogata (The University of
Tokyo) as part of BIRS workshop: Topology and Entanglement in Many-Body S
ystems\n\n\nAbstract\nI will talk about our trial on classification of SPT
phases in quantum statistical mechanics.\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5502/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kohtaro Kato (Nagoya University)
DTSTART;VALUE=DATE-TIME:20211013T010000Z
DTEND;VALUE=DATE-TIME:20211013T014500Z
DTSTAMP;VALUE=DATE-TIME:20220528T202146Z
UID:BIRS-21w5502/4
DESCRIPTION:Title: Entanglement bootstrap approach in 2D gapped spin systems\nby Koh
taro Kato (Nagoya University) as part of BIRS workshop: Topology and Entan
glement in Many-Body Systems\n\n\nAbstract\nQuantum phases (without symmet
ry) in two-dimensional (2D) gapped systems are expected to be classified i
nto different topologically ordered phases\, which cannot be described by
the conventional theory of symmetry-breaking. A vast amount of work has be
en dedicated to classify/characterize these new phases\, and nowadays\, it
is widely believed that all topologically ordered phases can be classifie
d by topological quantum field theory (TQFT). Although the existing analyt
ical studies as well as numerical studies are consistent with the predicti
on of this theory\, we still lack a general\, concrete proof that directly
shows that any 2D gapped quantum phases should be classified in this fram
ework. \n\nIn this talk\, we propose the entanglement bootstrap program t
o make progress on this important problem. In this program\, we posit that
local reduced density matrices of such systems obey a set of entropic ide
ntities followed by the area law of entanglement. We show that the axioms
of the fusion rules of anyon are derived from the entropic identities only
. We then discuss recent applications of this approach to S-matrix and cen
tral charges. We also discuss an obstacle of the universality of this appr
oach\, spurious topological entropy.\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5502/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bruno Nachtergaele (University of California\, Davis)
DTSTART;VALUE=DATE-TIME:20211013T160000Z
DTEND;VALUE=DATE-TIME:20211013T164500Z
DTSTAMP;VALUE=DATE-TIME:20220528T202146Z
UID:BIRS-21w5502/5
DESCRIPTION:Title: Spectral gaps\, gapped curves\, and stability\nby Bruno Nachterga
ele (University of California\, Davis) as part of BIRS workshop: Topology
and Entanglement in Many-Body Systems\n\n\nAbstract\nI discuss the stabili
ty of spectral gaps for quantum lattice systems subject to small perturbat
ions of the interactions defining the Hamiltonian and its connection to to
pological and symmetry-protected topological phases. I will review the cur
rent status of the problem and then discuss the application of recent resu
lts to the stability of a dimerized phases in a family of quantum spin cha
ins with O(n) symmetry and certain features of their phase diagram\, inclu
ding in the neighborhood of a non-frustration-free point. (Includes joint
work with Robert Sims and Amanda Young and with Jakob Bjoernberg\, Peter M
uehlbacher\, and Daniel Ueltschi).\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5502/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Levin (University of Chicago)
DTSTART;VALUE=DATE-TIME:20211013T173000Z
DTEND;VALUE=DATE-TIME:20211013T181500Z
DTSTAMP;VALUE=DATE-TIME:20220528T202146Z
UID:BIRS-21w5502/6
DESCRIPTION:Title: Stability of ground state degeneracy to long-range interactions\n
by Michael Levin (University of Chicago) as part of BIRS workshop: Topolog
y and Entanglement in Many-Body Systems\n\n\nAbstract\nSome gapped quantum
many-body systems have the interesting property that they have multiple n
early degenerate ground states with an energy splitting that is exponentia
lly small in the system size. Furthermore\, this nearly exact degeneracy i
s a robust phenomenon in the sense that it does not require fine tuning pa
rameters in the Hamiltonian. While this kind of nearly exact ground state
degeneracy is a well-established phenomenon for systems with short-range i
nteractions\, much less is known about long-range interactions (e.g.\, pow
er-law decaying interactions). In this talk\, I will present a rigorous re
sult showing that a robust\, exponentially small ground state splitting al
so occurs in some models with long-range interactions.\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5502/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Pérez-García (Complutense University of Madrid - ICMAT)
DTSTART;VALUE=DATE-TIME:20211014T160000Z
DTEND;VALUE=DATE-TIME:20211014T164500Z
DTSTAMP;VALUE=DATE-TIME:20220528T202146Z
UID:BIRS-21w5502/7
DESCRIPTION:Title: Bulk-boundary correspondence in Tensor Networks\nby David Pérez-
García (Complutense University of Madrid - ICMAT) as part of BIRS worksho
p: Topology and Entanglement in Many-Body Systems\n\n\nAbstract\nTensor Ne
tworks constitute a very rich family of states that is known to capture th
e low energy sector of locally interacting quantum systems. One of their m
ost interesting features is the existence of a rigorous bulk-boundary corr
espondence: interesting (and usually complex) bulk properties have an easi
er characterization at the boundary. Examples of such bulk properties incl
ude the existence of a spectral gap or the presence of topological order.
Both can be combined to shed new light in the problem of the existence of
self-correcting quantum memories in 2D.\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5502/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jeongwan Haah (Microsoft Research)
DTSTART;VALUE=DATE-TIME:20211014T173000Z
DTEND;VALUE=DATE-TIME:20211014T181500Z
DTSTAMP;VALUE=DATE-TIME:20220528T202146Z
UID:BIRS-21w5502/8
DESCRIPTION:Title: Gapping out a subalgebra and classifying Clifford QCAs\nby Jeongw
an Haah (Microsoft Research) as part of BIRS workshop: Topology and Entang
lement in Many-Body Systems\n\n\nAbstract\nA QCA is a locality preserving
automorphism of operator algebra on lattices. Such an automorphism is char
acterized by a subalgebra on a boundary. The existence of a maximal commut
ative set of local operators within the subalgebra restricts feasible QCAs
. From this approach\, we classify Clifford QCA in 3d\, the ones that map
every Pauli operator to another.\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5502/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Walter (University of Amsterdam)
DTSTART;VALUE=DATE-TIME:20211015T160000Z
DTEND;VALUE=DATE-TIME:20211015T164500Z
DTSTAMP;VALUE=DATE-TIME:20220528T202146Z
UID:BIRS-21w5502/9
DESCRIPTION:Title: Approximate QCAs and a converse to the Lieb-Robinson bounds\nby M
ichael Walter (University of Amsterdam) as part of BIRS workshop: Topology
and Entanglement in Many-Body Systems\n\n\nAbstract\nUnitary evolutions o
f quantum lattice systems that preserve locality are called "quantum cellu
lar automata"\, or QCAs. QCAs in one dimension have been completely classi
fied by an index theory. However\, physical systems often only preserve lo
cality approximately. For example\, Hamiltonian evolutions on the lattice
satisfy Lieb-Robinson bounds rather than strict locality. In this talk\, w
e will discuss QCAs that approximately preserve locality. As we will see\,
the index theory of 1D QCAs is robust even when considering these more ge
neral evolutions. As a consequence\, we also obtain a converse to the Lieb
-Robinson bounds in one dimension. Based on work with Daniel Ranard and Fr
eek Witteveen in arXiv:2012.00741.\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5502/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nikita Sopenko (Caltech)
DTSTART;VALUE=DATE-TIME:20211015T173000Z
DTEND;VALUE=DATE-TIME:20211015T181500Z
DTSTAMP;VALUE=DATE-TIME:20220528T202146Z
UID:BIRS-21w5502/10
DESCRIPTION:Title: Invariants for families of gapped ground states\nby Nikita Sopen
ko (Caltech) as part of BIRS workshop: Topology and Entanglement in Many-B
ody Systems\n\n\nAbstract\nI will talk about how to define invariants for
families of d-dimensional gapped ground states on the lattice known as Hig
her Berry classes. As an application I will show how to construct the inva
riant of 2d gapped ground states with semisimple Lie group symmetry G taki
ng values in H^3(G\,R) and show it’s quantization for invertible states.
\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5502/10/
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