A Memory Hierarchy for Many-Body Localization: Emulating the Thermodynamic Limit

TL;DR

This paper explores different ways to measure local memory in many-body localization, proposing a decoherence method to better emulate the thermodynamic limit and improve the detection of phase transition properties.

Contribution

It introduces a hierarchy of information-theoretic measures of memory, and demonstrates that decohering quantum quantities enhances the detection of localization transition criticality.

Findings

Holevo quantity outperforms imbalance in memory quantification

Decohering quantum measures aligns critical exponents with analytic predictions

Decoherence simplifies experimental detection by avoiding quantum state tomography

Abstract

Local memory - the ability to extract information from a subsystem about its initial state - is a central feature of many-body localization. We introduce, investigate, and compare several information-theoretic quantifications of memory and discover a hierarchical relationship among them. We also find that while the Holevo quantity is the most complete quantifier of memory, vastly outperforming the imbalance, its decohered counterpart is significantly better at capturing the critical properties of the many-body localization transition at small system sizes. This motivates our suggestion that one can emulate the thermodynamic limit by artifically decohering otherwise quantum quantities. Applying this method to the von Neumann entropy results in critical exponents consistent with analytic predictions, a feature missing from similar small finite-size system treatments. In addition, the decohering process makes experiments significantly simpler by avoiding quantum state tomography.