Spectral statistics of a minimal quantum glass model

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.

41 pages, 10 figures

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Cited by in corpus (9)

• Scale-invariant critical dynamics at eigenstate transitions
• A model of randomly-coupled Pauli spins
• Long-range spectral statistics of the Rosenzweig-Porter model
• Universal Properties of the Spectral Form Factor in Open Quantum Systems
• Re-entrant localization induced by short-range hopping in the fractal Rosenzweig-Porter Model
• Boundary Chaos: Spectral Form Factor
• Spectral anomalies and broken symmetries in maximally chaotic quantum maps
• Eigenstate Thermalization in 1+1-Dimensional SU(2) Lattice Gauge Theory Coupled with Dynamical Fermions
• Many-body spectral transitions through the lens of the variable-range SYK2 model