SciPost Physics

SciPost Phys. 10, 107 (2021) · published 17 May 2021

• doi: 10.21468/SciPostPhys.10.5.107
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Abstract

Disordered interacting spin chains that undergo a many-body localization transition are characterized by two limiting behaviors where the dynamics are chaotic and integrable. However, the transition region between them is not fully understood yet. We propose here a possible finite-size precursor of a critical point that shows a typical finite-size scaling and distinguishes between two different dynamical phases. The kurtosis excess of the diagonal fluctuations of the full one-dimensional momentum distribution from its microcanonical average is maximum at this singular point in the paradigmatic disordered $J_1$-$J_2$ model. For system sizes accessible to exact diagonalization, both the position and the size of this maximum scale linearly with the system size. Furthermore, we show that this singular point is found at the same disorder strength at which the Thouless and the Heisenberg energies coincide. Below this point, the spectral statistics follow the universal random matrix behavior up to the Thouless energy. Above it, no traces of chaotic behavior remain, and the spectral statistics are well described by a generalized semi-Poissonian model, eventually leading to the integrable Poissonian behavior. We provide, thus, an integrated scenario for the many-body localization transition, conjecturing that the critical point in the thermodynamic limit, if it exists, should be given by this value of disorder strength.

• Krajewski et al., Modeling sample-to-sample fluctuations of the gap ratio in finite disordered spin chains
  Phys. Rev. B 106, 014201 (2022) [Crossref]
• Šuntajs et al., Localization challenges quantum chaos in the finite two-dimensional Anderson model
  Phys. Rev. B 107, 064205 (2023) [Crossref]
• Šuntajs et al., Ergodicity Breaking Transition in Zero Dimensions
  Phys. Rev. Lett. 129, 060602 (2022) [Crossref]
• Šuntajs et al., Similarity between a many-body quantum avalanche model and the ultrametric random matrix model
  Phys. Rev. Research 6, 023030 (2024) [Crossref]
• Xu et al., Non-ergodic extended regime in random matrix ensembles: insights from eigenvalue spectra
  Sci Rep 13, 634 (2023) [Crossref]
• Rao, Approaching the Thouless energy and Griffiths regime in random spin systems by singular value decomposition
  Phys. Rev. B 105, 054207 (2022) [Crossref]
• Krajewski et al., Restoring Ergodicity in a Strongly Disordered Interacting Chain
  Phys. Rev. Lett. 129, 260601 (2022) [Crossref]
• Hita-Pérez et al., Missing levels in intermediate spectra
  J. Phys. A: Math. Theor. 56, 505702 (2023) [Crossref]
• Colmenarez et al., Subdiffusive Thouless time scaling in the Anderson model on random regular graphs
  Phys. Rev. B 105, 174207 (2022) [Crossref]
• Rao, Random matrix model for eigenvalue statistics in random spin systems
  Physica A: Statistical Mechanics and its Applications 590, 126689 126689 (2022) [Crossref]
• Vidmar et al., Phenomenology of Spectral Functions in Disordered Spin Chains at Infinite Temperature
  Phys. Rev. Lett. 127, 230603 (2021) [Crossref]
• Hopjan et al., Scale-Invariant Survival Probability at Eigenstate Transitions
  Phys. Rev. Lett. 131, 060404 (2023) [Crossref]
• Białous et al., Enhancement factor in the regime of semi-Poisson statistics in a singular microwave cavity
  Phys. Rev. E 106, 064208 (2022) [Crossref]
• Lóbez et al., Can we retrieve information from quantum thermalized states?
  J. Stat. Mech. 2021, 083104 (2021) [Crossref]