Information-Theoretic Memory Scaling in the Many-Body Localization Transition

TL;DR

This paper introduces the dynamical Holevo quantity as a comprehensive measure of local memory in many-body localization, revealing clear scaling behavior and critical exponents across the transition.

Contribution

It proposes the dynamical Holevo quantity as a new, optimal information-theoretic measure of local memory in many-body localization, with detailed scaling analysis.

Findings

Clear scaling behavior of the Holevo quantity at the transition

Determination of the transition point and critical exponents

Development of a two-parameter scaling ansatz

Abstract

A key feature of the many-body localized phase is the breaking of ergodicity and consequently the emergence of local memory; revealed as the local preservation of information over time. As memory is necessarily a time dependent concept, it has been partially captured by a few extant studies of dynamical quantities. However, these quantities are neither optimal, nor democratic with respect to input state; and as such a fundamental and complete information theoretic understanding of local memory in the context of many-body localization remains elusive. We introduce the dynamical Holevo quantity as the true quantifier of local memory, outlining its advantages over other quantities such as the imbalance or entanglement entropy. We find clear scaling behavior in its steady-state across the many-body localization transition, and determine a family of two-parameter scaling ans\"atze which captures this behavior. We perform a comprehensive finite size scaling analysis of this dynamical quantity extracting the transition point and scaling exponents.