The many-body localized phase of the quantum random energy model

TL;DR

This paper investigates the many-body localization-delocalization transition in the quantum random energy model, combining analytical methods and numerical validation to understand the critical behavior and eigenstate structure.

Contribution

It provides a detailed analysis of the MBLD transition in QREM using forward-scattering and replica techniques, and compares predictions with numerical results.

Findings

Transition line predictions agree with numerical results

Eigenstate structure varies continuously at the critical point

Evidence suggests a family of critical theories for the transition

Abstract

The random energy model (REM) provides a solvable mean-field description of the equilibrium spin glass transition. Its quantum sibling (the QREM), obtained by adding a transverse field to the REM, has similar properties and shows a spin glass phase for sufficiently small transverse field and temperature. In a recent work, some of us have shown that the QREM further exhibits a many-body localization - delocalization (MBLD) transition when viewed as a closed quantum system, evolving according to the quantum dynamics. This phase encloses the familiar equilibrium spin-glass phase. In this paper we study in detail the MBLD transition within the forward-scattering approximation and replica techniques. The predictions for the transition line are in good agreement with the exact diagonalization numerics. We also observe that the structure of the eigenstates at the MBLD critical point changes continuously with the energy density, raising the possibility of a family of critical theories for the MBLD transition.