Quantum Mutual Information as a Probe for Many-Body Localization

TL;DR

This paper shows that quantum mutual information (QMI) effectively detects many-body localization (MBL) and distinguishes it from Anderson insulators by analyzing static and dynamical properties in different models.

Contribution

It introduces QMI as a new tool for identifying localization transitions and characterizing phases in many-body quantum systems.

Findings

QMI decays exponentially in localized phases, defining a correlation length.

QMI remains localized in Anderson insulators but grows logarithmically in MBL phases after a quench.

QMI can distinguish between Anderson insulators and MBL phases dynamically.

Abstract

We demonstrate that the quantum mutual information (QMI) is a useful probe to study many-body localization (MBL). First, we focus on the detection of a metal--insulator transition for two different models, the noninteracting Aubry-Andr\'e-Harper model and the spinless fermionic disordered Hubbard chain. We find that the QMI in the localized phase decays exponentially with the distance between the regions traced out, allowing us to define a correlation length, which converges to the localization length in the case of one particle. Second, we show how the QMI can be used as a dynamical indicator to distinguish an Anderson insulator phase from an MBL phase. By studying the spread of the QMI after a global quench from a random product state, we show that the QMI does not spread in the Anderson insulator phase but grows logarithmically in time in the MBL phase.