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SUMMARY:Non-Hermitian symmetry-protected topological band theory - Simon L
 ieu\, Imperial College London 
DTSTART:20190502T131500Z
DTEND:20190502T141500Z
UID:TALK122395@talks.cam.ac.uk
CONTACT:Katarzyna Macieszczak
DESCRIPTION:Topological band theory was developed to predict and explain r
 obust features in the ground state electronic structure of insulators and 
 superconductors. Are these ideas applicable to open quantum systems? In th
 is talk\, I will discuss the topology of "non-Hermitian Hamiltonians" whic
 h evolve systems non-unitarily in time or space. While much of this formal
 ism has been successfully applied to dissipative classical photonics\, my 
 focus will be on its relevance to open quantum many-body theory. Specifica
 lly\, I will discuss progress to achieve "topologically-degenerate steady 
 states\," in analogy with the equilibrium paradigm of topologically-degene
 rate ground states. I provide an example where a non-Hermitian Majorana ze
 ro mode is responsible for this behavior in a partially-projected atomic s
 ystem. Current efforts are aimed at realizing robust degeneracies in the c
 omplex spectrum of the (Lindblad) master equation. From a mathematical poi
 nt of view\, non-Hermiticity of the Hamiltonian results in a richer set of
  topological symmetry classes. I highlight the importance of the "Bernard-
 LeClair" classes which generalize the Altland-Zirnbauer (AZ) classes in th
 e absence of Hermiticity. These classes represent a new direction in symme
 try-protected topological phases which go beyond the AZ and crystalline sy
 mmetries.
LOCATION:TCM Seminar Room\, Cavendish Laboratory
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