Many-body Localization Transition in Rokhsar-Kivelson-type wave functions

TL;DR

This paper introduces a family of Rokhsar-Kivelson wave functions based on classical spin glass models to study the many-body localization transition, revealing distinct entanglement regimes and multifractal behavior near the transition.

Contribution

It constructs a novel class of wave functions combining classical spin glass weights with random signs to explore MBL phase transition properties.

Findings

Identifies three regimes of entanglement scaling: thermal, constant, and sub-extensive.

Shows non-Gaussian fluctuations of Re9nyi entropies near the transition.

Demonstrates different transition points and scaling for Re9nyi entropies with different indices.

Abstract

We construct a family of many-body wave functions to study the many-body localization phase transition. The wave functions have a Rokhsar-Kivelson form, in which the weight for the configurations are chosen from the Gibbs weights of a classical spin glass model, known as the Random Energy Model, multiplied by a random sign structure to represent a highly excited state. These wave functions show a phase transition into an MBL phase. In addition, we see three regimes of entanglement scaling with subsystem size: scaling with entanglement corresponding to an infinite temperature thermal phase, constant scaling, and a sub-extensive scaling between these limits. Near the phase transition point, the fluctuations of the R\'enyi entropies are non-Gaussian. We find that R\'enyi entropies with different R\'enyi index transition into the MBL phase at different points and have different scaling behavior, suggesting a multifractal behavior.