Out of equilibrium Phase Diagram of the Quantum Random Energy Model

• URL: http://arxiv.org/abs/2009.09817v2
• Date: Fri, 12 Mar 2021 00:22:18 GMT
• Title: Out of equilibrium Phase Diagram of the Quantum Random Energy Model
• Authors: Giulio Biroli, Davide Facoetti, Marco Schir\'o, Marco Tarzia, Pierpaolo Vivo
• Abstract summary: We study the out-of-equilibrium phase diagram of the quantum version of Random Energy Model. We apply different theoretical methods tailored for high-dimensional lattices.
• Score: 7.775545390766461
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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