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Tenfold Way for Quadratic Lindbladians.

Published version
Peer-reviewed

Change log

Authors

Lieu, Simon 
McGinley, Maximilian  ORCID logo  https://orcid.org/0000-0003-3122-2207
Cooper, Nigel R 

Abstract

We uncover a topological classification applicable to open fermionic systems governed by a general class of Lindblad master equations. These "quadratic Lindbladians" can be captured by a non-Hermitian single-particle matrix which describes internal dynamics as well as system-environment coupling. We show that this matrix must belong to one of ten non-Hermitian Bernard-LeClair symmetry classes which reduce to the Altland-Zirnbauer classes in the closed limit. The Lindblad spectrum admits a topological classification, which we show results in gapless edge excitations with finite lifetimes. Unlike previous studies of purely Hamiltonian or purely dissipative evolution, these topological edge modes are unconnected to the form of the steady state. We provide one-dimensional examples where the addition of dissipators can either preserve or destroy the closed classification of a model, highlighting the sensitivity of topological properties to details of the system-environment coupling.

Description

Keywords

cond-mat.mes-hall, cond-mat.mes-hall, cond-mat.quant-gas, cond-mat.str-el, quant-ph

Journal Title

Phys Rev Lett

Conference Name

Journal ISSN

0031-9007
1079-7114

Volume Title

124

Publisher

American Physical Society (APS)

Rights

All rights reserved
Sponsorship
Simons Foundation (511029)
Engineering and Physical Sciences Research Council (EP/P034616/1)