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Article Dans Une Revue Physical Review B Année : 2021

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

Giulio Biroli
Marco Tarzia
Pierpaolo Vivo

Résumé

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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Dates et versions

hal-03425654 , version 1 (10-11-2021)
hal-03425654 , version 2 (23-11-2021)

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Giulio Biroli, Davide Facoetti, Marco Schiró, Marco Tarzia, Pierpaolo Vivo. Out-of-equilibrium phase diagram of the quantum random energy model. Physical Review B, 2021, 103 (1), pp.014204. ⟨10.1103/PhysRevB.103.014204⟩. ⟨hal-03425654v2⟩
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