Out-of-equilibrium phase diagram of the quantum random energy model

TY - JOUR

T1 - Out-of-equilibrium phase diagram of the quantum random energy model

AU - Biroli, Giulio

AU - Facoetti, Davide

AU - Schiró, Marco

AU - Tarzia, Marco

AU - Vivo, Pierpaolo

N1 - Funding Information: We warmly thank L. Ioffe for helpful discussions. This work was partially supported by the Simons Foundation through Grant No. 454935 (G.B.). D.F. was partially supported by the EPSRC (CANES, Grant No. EP/L015854/1) and the European Research Council under the European Union's Horizon 2020 research and innovation program (Grant Agreement No. 723955, GlassUniversality). Publisher Copyright: © 2021 American Physical Society. Copyright: Copyright 2021 Elsevier B.V., All rights reserved.

PY - 2021/1/29

Y1 - 2021/1/29

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85100177817&partnerID=8YFLogxK

U2 - 10.1103/PhysRevB.103.014204

DO - 10.1103/PhysRevB.103.014204

M3 - Article

AN - SCOPUS:85100177817

SN - 2469-9950

VL - 103

JO - Physical Review B

JF - Physical Review B

IS - 1

M1 - 014204

ER -