title: Many-body mobility edge in a mean-field quantum spin glass.
abstract: The quantum random energy model provides a mean-field description of the equilibrium spin glass transition. We show that it further exhibits a many-body localization-delocalization (MBLD) transition when viewed as a closed quantum system. The mean-field structure of the model allows an analytically tractable description of the MBLD transition using the forward-scattering approximation and replica techniques. The predictions are in good agreement with the numerics. The MBLD transition lies at energy density significantly above the equilibrium spin glass transition, indicating that the closed system dynamics freezes well outside of the traditional glass phase. We also observe that the structure of the eigenstates at the MBLD critical point changes continuously with the energy density, raising the possibility of a family of critical theories for the MBLD transition.
authors.affiliation: Department of Physics, University of Washington, Seattle, Washington 98195, USA and Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada.
authors.forename: C R
authors.initials: CR
authors.lastname: Laumann
authors.affiliation: Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA.
authors.forename: A
authors.initials: A
authors.lastname: Pal
authors.affiliation: Physics Department, Princeton University, Princeton, New Jersey 08542, USA and Physics Department, Columbia University, New York, New York 10027, USA and ITS, Graduate Center, City University of New York, New York, New York 10016, USA and INFN, Sezione di Trieste, Via Valerio 2, Trieste 34151, Italy.
authors.forename: A
authors.initials: A
authors.lastname: Scardicchio