Localization and chaos in a spin glass model with random fields: Mapping to the localization problem in a Bethe lattice with a correlated disorder

TL;DR

This paper maps a quantum spin glass model with random fields to an Anderson localization problem on a Bethe lattice, revealing how interactions and temperature influence localization and delocalization regimes.

Contribution

It provides an analytical solution linking many-body localization in a spin glass to Anderson localization, highlighting the impact of interactions and temperature on localization transitions.

Findings

Localization transition is sensitive to interaction-field relationship.

Decreasing temperature enhances localization.

Universal behavior of localization transition in spin glass phase.

Abstract

The analytical solution of a many-body localization problem in a quantum Sherrington-Kirkpatrick spin glass model in a random longitudinal field is proposed matching the problem with a model of Anderson localization in a Bethe lattice. The localization transition is dramatically sensitive to the relationship between interspin interaction and random field revealing different regimes in which the interaction can either suppress or enhance the delocalization. The localization is enhanced by decreasing the temperature and the localization transition shows a remarkable universality in a spin glass phase. The observed trends should be qualitatively relevant for other systems showing many-body localization.