Spectral statistics of a minimal quantum glass model

TL;DR

This paper introduces the Block Rosenzweig-Porter (BRP) model, a minimal quantum model that captures the transition from glassy to chaotic behavior, and analyzes its spectral form factors across all timescales.

Contribution

The paper generalizes the RP model to the BRP model, enabling the study of the transition from glassy to chaotic quantum states through spectral analysis.

Findings

BRP model exhibits a crossover from glassy to chaotic behavior.

Spectral form factors show a change in ramp slope indicating the transition.

Compared to RP, BRP captures more complex quantum state dynamics.

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. 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 slope of the ramp of the spectral form factor.