SciPost Physics

SciPost Phys. 15, 084 (2023) · published 7 September 2023

• doi: 10.21468/SciPostPhys.15.3.084
• pdf
• BiBTeX
• RIS
• Submissions/Reports
• 

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.

• Zhou et al., General properties of the spectral form factor in open quantum systems
  Front. Phys. 19, 31202 (2024) [Crossref]
• Hanada et al., A model of randomly-coupled Pauli spins
  J. High Energ. Phys. 2024, 280 (2024) [Crossref]
• Wei et al., Generalized spectral form factor in random matrix theory
  Phys. Rev. E 109, 064208 (2024) [Crossref]
• Hopjan et al., Scale-invariant critical dynamics at eigenstate transitions
  Phys. Rev. Research 5, 043301 (2023) [Crossref]
• Fritzsch et al., Universal spectral correlations in interacting chaotic few-body quantum systems
  Phys. Rev. E 109, 014202 (2024) [Crossref]
• Buijsman, Long-range spectral statistics of the Rosenzweig-Porter model
  Phys. Rev. B 109, 024205 (2024) [Crossref]
• Swingle et al., Bosonic model of quantum holography
  Phys. Rev. B 109, 094206 (2024) [Crossref]