Multipoint entanglement in disordered systems

TL;DR

This paper introduces a method to analyze excited states in disordered many-body systems using entanglement structures, revealing differences between thermal and localized phases through measures like mutual information.

Contribution

It develops a framework based on spatial entanglement to distinguish phases in disordered systems and applies it to both non-interacting and interacting models, including experimental scenarios.

Findings

Mutual information is finite in insulators and vanishes in ergodic phases.

The Codification Volume effectively measures correlation length.

Localized phases show significant quantum information delocalization in some initial states.

Abstract

We develop an approach to characterize excited states of disordered many-body systems using spatially resolved structures of entanglement. We show that the behavior of the mutual information (MI) between two parties of a many-body system can signal a qualitative difference between thermal and localized phases -- MI is finite in insulators while it approaches zero in the thermodynamic limit in the ergodic phase. Related quantities, such as the recently introduced Codification Volume (CV), are shown to be suitable to quantify the correlation length of the system. These ideas are illustrated using prototypical non-interacting wavefunctions of localized and extended particles and then applied to characterize states of strongly excited interacting spin chains. We especially focus on evolution of spatial structure of quantum information between high temperature diffusive and many-body localized phases believed to exist in these models. We study MI as a function of disorder strength both averaged over the eigenstates and in time-evolved product states drawn from continuously deformed family of initial states realizable experimentally. As expected, spectral and time-evolved averages coincide inside the ergodic phase and differ significantly outside. We also highlight dispersion among the initial states \emph{within} the localized phase -- some of these show considerable generation and delocalization of quantum information.