Model of level statistics for disordered interacting quantum many-body systems

Abstract

We numerically study level statistics of disordered interacting quantum many-body systems. A two-parameter plasma model which controls level repulsion exponent $\beta$ and range $h$ of interactions between eigenvalues is shown to reproduce accurately features of level statistics across the transition from ergodic to many-body localized phase. Analysis of higher order spacing ratios indicates that the considered $\beta$-$h$ model accounts even for long range spectral correlations and allows to obtain a clear picture of the flow of level statistics across the transition. Comparing spectral form factors of $\beta$-$h$ model and of a system in the ergodic-MBL crossover, we show that the range of effective interactions between eigenvalues $h$ is related to the Thouless time which marks the onset of quantum chaotic behavior of the system. Analysis of level statistics of random quantum circuit which hosts chaotic and localized phases supports the claim that $\beta$-$h$ model grasps universal features of level statistics in transition between ergodic and many-body localized phases also for systems breaking time-reversal invariance.

normalization in eq. 4 added, 10pp, 12 figs accepted in PRB

References in corpus (25)

• Many body localization and thermalization in quantum statistical mechanics
• Anderson Transitions
• Localization of interacting fermions at high temperature
• Many-body localization edge in the random-field Heisenberg chain
• Many body localization in Heisenberg XXZ magnet in a random field
• Phenomenology of fully many-body-localized systems
• Integrals of motion in the Many-Body localized phase
• Spectral signatures of many-body localization with interacting photons
• Anomalous diffusion and Griffiths effects near the many-body localization transition
• Absence of diffusion in an interacting system of spinless fermions on a one-dimensional disordered lattice
• Ergodicity breaking in a model showing many-body localization
• Anomalous thermalization in ergodic systems
• Can we study the many-body localisation transition?
• Spectral statistics and many-body quantum chaos with conserved charge
• Many-body localization due to random interactions
• Many-body localization in infinite chains
• Renormalization-group study of the many-body localization transition in one dimension
• Poisson to GOE transition in the distribution of the ratio of consecutive level spacings
• Universal dynamics of density correlations at the transition to many-body localized state
• Many-body localization in presence of cavity mediated long-range interactions
• Many Body Localization Due to Correlated Disorder in Fock Space
• Energy level dynamics across the many-body localization transition
• Statistics of correlation functions in the random Heisenberg chain
• Finite-Range Coulomb Gas Models II: Applications to Quantum Kicked Rotors and Banded Random Matrices
• Finite-Range Coulomb Gas Models I: Some Analytical Results

Cited by in corpus (45)

• Thouless time analysis of Anderson and many-body localization transitions
• Ergodicity Breaking Transition in Finite Disordered Spin Chains
• Challenges to observation of many-body localization
• Polynomially filtered exact diagonalization approach to many-body localization
• Many-Body Localization in the Age of Classical Computing
• Rainbow Scars: From Area to Volume Law
• Many-body localization from a one-particle perspective in the disordered 1D Bose-Hubbard model
• Universal spectral form factor for many-body localization
• Stability of many-body localization in Floquet systems
• Universality in Anderson localization on random graphs with varying connectivity
• Distribution of the Ratio of Consecutive Level Spacings for Different Symmetries and Degrees of Chaos
• Many-body localization in tilted and harmonic potentials
• Many-body localization transition in large quantum spin chains: The mobility edge
• Constraints induced delocalization
• Higher-order level spacings in random matrix theory based on Wigner's conjecture
• Catching thermal avalanches in the disordered XXZ model
• Detecting ergodic bubbles at the crossover to many-body localization using neural networks
• Signatures of a critical point in the many-body localization transition
• Long-range level correlations in quantum systems with finite Hilbert space dimension
• Dynamics of spectral correlations in the entanglement Hamiltonian of the Aubry-André-Harper model
• Many-Body Mobility Edge in Quantum Sun models
• Critical Level Statistics at the Many-Body Localization Transition Region
• Nonstabilizerness dynamics in many-body localized systems
• Many-body localization with synthetic gauge fields in disordered Hubbard chains
• Long-range spectral statistics of the Rosenzweig-Porter model
• Sensitivity of the spectral form factor to short-range level statistics
• On intermediate statistics across many-body localization transition
• Quantum chaos and level dynamics
• Decomposing the Spectral Form Factor
• Many-body localization crossover is sharper in quasiperiodic spin chains
• Power-Law Random Banded Matrix Ensemble as the Effective Model for Many-Body Localization Transition
• Phenomenology of many-body localization in bond-disordered spin chains
• Quantum Chaos in Random Ising Networks
• Scaling of the Reduced Energy Spectrum of Random Matrix Ensemble
• Many-body localization regime for cavity induced long-range interacting models
• Random Matrix Model for Eigenvalue Statistics in Random Spin Systems
• Tracking locality in time evolution of disordered systems
• Modelling sample-to-sample fluctuations of the gap ratio in finite disordered spin chains
• Long-ranged spectral correlations in eigenstate phases
• Universal scaling of higher-order spacing ratios in Gaussian random matrices
• Anomalous energy correlations and spectral form factor in the nonergodic phase of the $\beta$-ensemble
• A Complex Network Analysis on The Eigenvalue Spectra of Random Spin Systems
• Higher-Order Krylov State Complexity in Random Matrix Quenches
• Surmise for random matrices' level spacing distributions beyond nearest-neighbors
• Crystalline Spectral Form Factors