Liouvillian-gap analysis of open quantum many-body systems in the weak dissipation limit

Abstract: Recent experiments have reported that novel physics emerge in open quantum many-body sys- tems due to an interplay of interactions and dissipation, which stimulate theoretical studies of the many-body Lindblad equation. Although the strong dissipation regime receives considerable in- terest in this context, this work focuses on the weak bulk dissipation. By examining the spectral property of the many-body Lindblad generator for specific models, we find that its spectral gap shows singularity in the weak dissipation limit when the thermodynamic limit is taken first. Based on analytical arguments and numerical calculations, we conjecture that such a singularity is generic in bulk-dissipated quantum many-body systems and is related to the concept of the Ruelle-Pollicott resonance in chaos theory, which determines the timescale of thermalization of an isolated system. This conjecture suggests that the many-body Lindblad equation in the weak dissipation regime contains nontrivial information on intrinsic properties of a quantum many-body system.