On intermediate statistics across many-body localization transition

Abstract

The level statistics in the transition between delocalized and localized {phases of} many body interacting systems is {considered}. We recall the joint probability distribution for eigenvalues resulting from the statistical mechanics for energy level dynamics as introduced by Pechukas and Yukawa. The resulting single parameter analytic distribution is probed numerically {via Monte Carlo method}. The resulting higher order spacing ratios are compared with data coming from different {quantum many body systems}. It is found that this Pechukas-Yukawa distribution compares favorably with {$\beta$--Gaussian ensemble -- a single parameter model of level statistics proposed recently in the context of disordered many-body systems.} {Moreover, the Pechukas-Yukawa distribution is also} only slightly inferior to the two-parameter $\beta$-h ansatz shown {earlier} to reproduce {level statistics of} physical systems remarkably well.

Version accepted for publication in Fritz Haake memorial volume of Journal of Physics A

References in corpus (9)

• Many body localization and thermalization in quantum statistical mechanics
• Localization of interacting fermions at high temperature
• Many-body localization edge in the random-field Heisenberg chain
• The distribution of the ratio of consecutive level spacings in random matrix ensembles
• Semiclassical Foundation of Universality in Quantum Chaos
• Periodic-Orbit Theory of Universality in Quantum Chaos
• Periodic-Orbit Theory of Level Correlations
• Many-body localization due to random interactions
• Poisson to GOE transition in the distribution of the ratio of consecutive level spacings

Cited by in corpus (4)

• Resonant energy scales and local observables in the many-body localised phase
• Signatures of quantum chaos in low-energy mixtures of few fermions
• Tracking locality in time evolution of disordered systems
• Universal scaling of higher-order spacing ratios in Gaussian random matrices