Out of equilibrium Phase Diagram of the Quantum Random Energy Model
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.
Keywords
Cite
@article{arxiv.2009.09817,
title = {Out of equilibrium Phase Diagram of the Quantum Random Energy Model},
author = {Giulio Biroli and Davide Facoetti and Marco Schiró and Marco Tarzia and Pierpaolo Vivo},
journal= {arXiv preprint arXiv:2009.09817},
year = {2021}
}
Comments
21 pages, 13 figures