Out of equilibrium Phase Diagram of the Quantum Random Energy Model

TL;DR

This study explores the out-of-equilibrium phase diagram of the quantum Random Energy Model, revealing three dynamical phases and transitions using high-dimensional theoretical methods, advancing understanding of quantum spin glasses.

Contribution

It introduces a detailed analysis of the quantum REM's dynamical phases and transitions using novel high-dimensional approximation techniques.

Findings

Identification of three distinct dynamical phases: localized, ergodic, and multifractal.

Discovery of two transition lines separating these phases.

Characterization of the multifractal 'bad metal' phase with diverging eigenfunction volume.

Abstract

In this paper we study the out-of-equilibrium phase diagram of the quantum version of Derrida's Random Energy Model, which is the simplest model of mean-field spin glasses. We interpret its corresponding quantum dynamics in Fock space as a one-particle problem in very high dimension to which we apply different theoretical methods tailored for high-dimensional lattices: the Forward-Scattering Approximation, a mapping to the Rosenzweig-Porter model, and the cavity method. Our results indicate the existence of two transition lines and three distinct dynamical phases: a completely many-body localized phase at low energy, a fully ergodic phase at high energy, and a multifractal "bad metal" phase at intermediate energy. In the latter, eigenfunctions occupy a diverging volume, yet an exponentially vanishing fraction of the total Hilbert space. We discuss the limitations of our approximations and the relationship with previous studies.