Localization of Lindbladian Fermions

Author:

Foster Thompson, Yi Huang, Alex Kamenev

Keyword:

Condensed Matter, Disordered Systems and Neural Networks, Disordered Systems and Neural Networks (cond-mat.dis-nn)

journal:

date:

2024-01-25 00:00:00

Abstract

We study a Lindbladian generalization of the Anderson model of localization that describes disordered free fermions coupled to a disordered environment. From finite size scaling of both eigenvalue statistics and participation ratio, we identify local- ization transitions in both the non-Hermitian Lindbladian spectrum, which governs transient relaxation dynamics, and in the Hermitian stationary state density ma- trix. These localization transitions occur at different critical values of Hamiltonian and dissipative disorder strength, implying the existence of atypical phases with a mixture of localized and delocalized features. We find this phenomenon is robust to changes to the value of the dissipative spectral gap.

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