Random Matrix Ensemble for the Level Statistics of Many-Body Localization

Abstract

We numerically study the level statistics of the Gaussian $\beta$ ensemble. These statistics generalize Wigner-Dyson level statistics from the discrete set of Dyson indices $\beta =1,2,4$ to the continuous range $0<\beta <\infty$. The Gaussian $\beta$ ensemble covers Poissonian level statistics for $\beta \to 0$, and provides a smooth interpolation between Poissonian and Wigner-Dyson level statistics. We establish the physical relevance of the level statistics of the Gaussian $\beta$ ensemble by showing near-perfect agreement with the level statistics of a paradigmatic model in studies on many-body localization over the entire crossover range from the thermal to the many-body localized phase. In addition, we show similar agreement for a related Hamiltonian with broken time-reversal symmetry.

arXiv comment6 pages, 5 figures

References in corpus (38)

• Random Matrix Theories in Quantum Physics: Common Concepts
• Metal-insulator transition in a weakly interacting many-electron system with localized single-particle states
• Localization of interacting fermions at high temperature
• The many-body localization phase transition
• Many-body localization edge in the random-field Heisenberg chain
• The distribution of the ratio of consecutive level spacings in random matrix ensembles
• On Many-Body Localization for Quantum Spin Chains
• Matrix Models for Beta Ensembles
• Anomalous diffusion and Griffiths effects near the many-body localization transition
• Recent progress in many-body localization
• Absence of diffusion in an interacting system of spinless fermions on a one-dimensional disordered lattice
• Random Matrices and Chaos in Nuclear Physics
• The Ergodic Side of the Many-Body Localization Transition
• Semiclassical Foundation of Universality in Quantum Chaos
• Spectral statistics across the many-body localization transition
• Critical Properties of the Many-Body Localization Transition
• Many-body quantum chaos: Analytic connection to random matrix theory
• New Class of Random Matrix Ensembles with Multifractal Eigenvectors
• Poisson versus GOE statistics in integrable and non-integrable quantum hamiltonian
• Supersymmetric SYK model and random matrix theory
• Chaotic-Integrable Transition in the Sachdev-Ye-Kitaev Model
• Anomalous Thouless energy and critical statistics on the metallic side of the many-body localization transition
• A generalized ensemble of random matrices
• Global spectrum fluctuations for the $\beta$-Hermite and $\beta$-Laguerre ensembles via matrix models
• Higher order spacing ratios in random matrix theory and complex quantum systems
• Universality and the QCD Anderson Transition
• Non-ergodicity in the Anisotropic Dicke model
• From closed to open 1D Anderson model: Transport versus spectral statistics
• Wigner-Poisson statistics of topological transitions in a Josephson junction
• Chaos and regularity in the doubly magic nucleus 208Pb
• The localization transition in SU(3) gauge theory
• Stringent Numerical Test of the Poisson Distribution for Finite Quantum Integrable Hamiltonians
• Nearest-neigbor spacing distributions of the beta-Hermite ensemble of random matrices
• A random matrix decimation procedure relating $\beta =2/(r+1)$ to $\beta =2(r+1)$
• Finite-size scaling with respect to interaction and disorder strength at the many-body localization transition
• Many-Body Localization and Level Repulsion
• Semiclassical approach to discrete symmetries in quantum chaos
• On invariant 2x2 β-ensembles of random matrices

Cited by in corpus (45)

• Quantum chaos challenges many-body localization
• Thouless time analysis of Anderson and many-body localization transitions
• Ergodicity Breaking Transition in Finite Disordered Spin Chains
• Complex Spacing Ratios: A Signature of Dissipative Quantum Chaos
• Many-Body Localization in the Age of Classical Computing
• Rainbow Scars: From Area to Volume Law
• Model of level statistics for disordered interacting quantum many-body systems
• Universal spectral form factor for many-body localization
• Distribution of the Ratio of Consecutive Level Spacings for Different Symmetries and Degrees of Chaos
• Random generators of Markovian evolution: A quantum-classical transition by superdecoherence
• Quantum State Complexity in Computationally Tractable Quantum Circuits
• Higher-order level spacings in random matrix theory based on Wigner's conjecture
• Thouless Energy Challenges Thermalization on the Ergodic Side of the Many-Body Localization Transition
• Krylov space approach to Singular Value Decomposition in non-Hermitian systems
• Signatures of quantum chaos in low-energy mixtures of few fermions
• Eigenvalue Statistics for Generalized Symmetric and Hermitian Matrices
• Superposition and higher-order spacing ratios in random matrix theory with application to complex systems
• Critical Level Statistics at the Many-Body Localization Transition Region
• On intermediate statistics across many-body localization transition
• Long-range spectral statistics of the Rosenzweig-Porter model
• Two transitions in complex eigenvalue statistics: Hermiticity and integrability breaking
• Quantum chaos and level dynamics
• Power-Law Random Banded Matrix Ensemble as the Effective Model for Many-Body Localization Transition
• Scaling of the Reduced Energy Spectrum of Random Matrix Ensemble
• Ground-state energy distribution of disordered many-body quantum systems
• Phenomenology of many-body localization in bond-disordered spin chains
• Eigenvalue ratio statistics of complex networks: Disorder vs. Randomness
• Higher-order gap ratios of singular values in open quantum systems
• Random Matrix Model for Eigenvalue Statistics in Random Spin Systems
• Characterization of many-body mobility edges with random matrices
• Single-particle localization in a two-dimensional Rydberg spin system
• Hole probability for noninteracting fermions in a $d$-dimensional trap
• Long-ranged spectral correlations in eigenstate phases
• Dynamics of quantum coherence in many-body localized systems
• Free Probability approach to spectral and operator statistics in Rosenzweig-Porter random matrix ensembles
• Tracking locality in time evolution of disordered systems
• Universal scaling of higher-order spacing ratios in Gaussian random matrices
• Efficient circular Dyson Brownian motion algorithm
• Power-law banded random matrix ensemble as a model for quantum many-body Hamiltonians
• Ensemble-averaged mean-field many-body level density: an indicator of integrable versus chaotic single-particle dynamics
• Robustness and Independence of the Eigenstates with respect to the Boundary Conditions across a Delocalization-Localization Phase Transition
• Surmise for random matrices' level spacing distributions beyond nearest-neighbors
• Higher-Order Krylov State Complexity in Random Matrix Quenches
• Crystalline Spectral Form Factors
• Quantum Lyapunov exponents and complex spacing ratios: two measures of Dissipative Quantum Chaos