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

Giulio Biroli, Davide Facoetti, Marco Schiró, Marco Tarzia, Pierpaolo Vivo

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12 Citations (Scopus)
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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.

Original languageEnglish
Article number014204
JournalPhysical Review B
Issue number1
Publication statusPublished - 29 Jan 2021


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