Spectral statistics of a minimal quantum glass model

Author:

Barney Richard1,Winer Michael1,Baldwin Christopher L.1,Swingle Brian2,Galitski Victor31

Affiliation:

1. Joint Quantum Institute

2. Brandeis University

3. Flatiron Institute

Abstract

Glasses have the interesting feature of being neither integrable nor fully chaotic. They thermalize quickly within a subspace but thermalize much more slowly across the full space due to high free energy barriers which partition the configuration space into sectors. Past works have examined the Rosenzweig-Porter (RP) model as a minimal quantum model which transitions from localized to chaotic behavior. In this work we generalize the RP model in such a way that it becomes a minimal model which transitions from glassy to chaotic behavior, which we term the “Block Rosenzweig-Porter” (BRP) model. We calculate the spectral form factors of both models at all timescales larger than the inverse spectral width. Whereas the RP model exhibits a crossover from localized to ergodic behavior at the Thouless timescale, the new BRP model instead crosses over from glassy to fully chaotic behavior, as seen by a change in the steepness of the ramp of the spectral form factor.

Funder

Advanced Scientific Computing Research

Air Force Office of Scientific Research

Army Research Office

Defense Advanced Research Projects Agency

Joint Quantum Institute

National Science Foundation

Office of Science

Simons Foundation

United States Department of Energy

Publisher

Stichting SciPost

Subject

General Physics and Astronomy

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