The distribution of the ratio of consecutive level spacings in random matrix ensembles

Abstract

We derive expressions for the probability distribution of the ratio of two consecutive level spacings for the classical ensembles of random matrices. This ratio distribution was recently introduced to study spectral properties of many-body problems, as, contrary to the standard level spacing distributions, it does not depend on the local density of states. Our Wigner-like surmises are shown to be very accurate when compared to numerics and exact calculations in the large matrix size limit. Quantitative improvements are found through a polynomial expansion. Examples from a quantum many-body lattice model and from zeros of the Riemann zeta function are presented.

5 pages, 4 figures

References in corpus (4)

• Localization of interacting fermions at high temperature
• Introduction to Random Matrices - Theory and Practice
• Quantum chaos and thermalization in gapped systems
• Statistical properties of the spectrum the extended Bose-Hubbard model

Cited by in corpus (22)

• Many-body localization edge in the random-field Heisenberg chain
• Spectral signatures of many-body localization with interacting photons
• Many-body localization due to random interactions
• A Floquet Model for the Many-Body Localization Transition
• Complete random matrix classification of SYK models with $\mathcal{N}=0$, $1$ and $2$ supersymmetry
• Robustness of delocalization to the inclusion of soft constraints in long-range random models
• Drive Induced Delocalization in Aubry-André Model
• Non-ergodicity in the Anisotropic Dicke model
• Quantum quenches and many-body localization in the thermodynamic limit
• Poisson to GOE transition in the distribution of the ratio of consecutive level spacings
• The eigenstate thermalization hypothesis in constrained Hilbert spaces: a case study in non-Abelian anyon chains
• Irreversibility and Entanglement Spectrum Statistics in Quantum Circuits
• Chaos and regularity in the doubly magic nucleus 208Pb
• Energy level dynamics across the many-body localization transition
• Many-body localization for randomly interacting bosons
• Many-body localization in Ising models with random long-range interactions
• Eigenstate Thermalization and Representative States on Subsystems
• Quantum many-body dynamics on the star graph
• Few-boson localization in a continuum with speckle disorder
• Many-body delocalization with random vector potentials
• Threshold coupling strength for equilibration between small systems
• Disordered statistical physics in low dimensions: extremes, glass transition, and localization