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arXiv · 2009.09817

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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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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Giulio Biroli, Davide Facoetti, Marco Schiró, Marco Tarzia, Pierpaolo Vivo. 2021-03-12. Out of equilibrium Phase Diagram of the Quantum Random Energy Model. https://doi.org/10.1103/physrevb.103.014204

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