title: Many-body localization in imperfectly isolated quantum systems.
abstract: We use numerical exact diagonalization to analyze which aspects of the many-body localization phenomenon survive in an imperfectly isolated setting, when the system of interest is weakly coupled to a thermalizing environment. We show that widely used diagnostics (such as many-body level statistics and expectation values in exact eigenstates) cease to show signatures of many-body localization above a critical coupling that is exponentially small in the size of the environment. However, we also identify alternative diagnostics for many-body localization, in the spectral functions of local operators. Diagnostics include a discrete spectrum and a hierarchy of energy gaps, including a universal gap at zero frequency. These alternative diagnostics are shown to be robust, and continue to show signatures of many-body localization as long as the coupling to the bath is weaker than the characteristic energy scales in the system. We also examine how these signatures disappear when the coupling to the environment becomes larger than the characteristic energy scales of the system.
authors.affiliation: Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA.
authors.forename: Sonika
authors.initials: S
authors.lastname: Johri
authors.affiliation: Princeton Center for Theoretical Science, Princeton University, Princeton, New Jersey 08544, USA.
authors.forename: Rahul
authors.initials: R
authors.lastname: Nandkishore
authors.affiliation: Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA.|School of Natural Sciences, Institute for Advanced Study, Princeton, New Jersey 08540, USA.
authors.forename: R N
authors.initials: RN
authors.lastname: Bhatt