Spectral features of a many-body localized system weakly coupled to a heat bath

Understand

We study many-body-localized (MBL) systems that are weakly coupled to thermalizing environments, focusing on the spectral functions of local operators.

• We argue that these spectral functions carry signatures of localization even away from the limit of perfectly isolated systems.
• We find that, in the limit of vanishing coupling to a bath, MBL systems come in two varieties, with either discrete or continuous local spectra.
• Both varieties of MBL systems exhibit a "soft gap" at zero frequency in the spatially-averaged spectral functions of local operators, which serves as a diagnostic for localization.