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CATEGORIES:Theory of Condensed Matter
SUMMARY:Non-Hermitian symmetry-protected topological band
theory - Simon Lieu\, Imperial College London
DTSTART;TZID=Europe/London:20190502T141500
DTEND;TZID=Europe/London:20190502T151500
UID:TALK122395AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/122395
DESCRIPTION:Topological band theory was developed to predict a
nd explain robust features in the ground state ele
ctronic structure of insulators and superconductor
s. Are these ideas applicable to open quantum syst
ems? In this talk\, I will discuss the topology of
"non-Hermitian Hamiltonians" which evolve systems
non-unitarily in time or space. While much of thi
s formalism has been successfully applied to dissi
pative classical photonics\, my focus will be on i
ts relevance to open quantum many-body theory. Spe
cifically\, I will discuss progress to achieve "to
pologically-degenerate steady states\," in analogy
with the equilibrium paradigm of topologically-de
generate ground states. I provide an example where
a non-Hermitian Majorana zero mode is responsible
for this behavior in a partially-projected atomic
system. Current efforts are aimed at realizing ro
bust degeneracies in the complex spectrum of the (
Lindblad) master equation. From a mathematical poi
nt of view\, non-Hermiticity of the Hamiltonian re
sults in a richer set of topological symmetry clas
ses. I highlight the importance of the "Bernard-Le
Clair" classes which generalize the Altland-Zirnba
uer (AZ) classes in the absence of Hermiticity. Th
ese classes represent a new direction in symmetry-
protected topological phases which go beyond the A
Z and crystalline symmetries.
LOCATION:TCM Seminar Room\, Cavendish Laboratory
CONTACT:Katarzyna Macieszczak
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