Many-body localization and thermalization: Insights from the entanglement spectrum

Abstract

The statistical physics of well isolated nonequilibrium quantum systems has been drawing intense interest recently, providing new paradigms for understanding equilibration and ergodicity (and failure thereof). Tools from the field of quantum information, such as quantum entanglement, have been instrumental in this development. Past investigations of the entanglement structure in localized and thermalizing phases have focused on diagnostics, such as entanglement entropy, which provide a useful but only partial characterization of the pattern of entanglement. In this work, inspired by random matrix theory, the authors examine localization and thermalization through the lens of the entanglement spectrum. This approach provides a complete characterization of the pattern of entanglement and yields new insights into many-body localization, thermalization, and nonequilibrium statistical mechanics.