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

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• Optimal quantum reservoir learning in proximity to universality
• Proof of the absence of local conserved quantities in general spin-1/2 chains with symmetric nearest-neighbor interaction
• Detecting quantum chaos via pseudo-entropy
• Coexistence of Anderson Localization and Quantum Scarring in Two Dimensions
• Quantum quenches across continuous and first-order quantum transitions in one-dimensional quantum Ising models
• Appearance of Random Matrix Theory in Deep Learning
• Universality in Non-Equilibrium Quantum Systems
• Numerical evidence for the non-Abelian eigenstate thermalization hypothesis
• Spectral anomalies and broken symmetries in maximally chaotic quantum maps
• Weak vs. strong breaking of integrability in interacting scalar quantum field theories
• Probing Electron Localization and Delocalization in the Selective Long-Range Tight-Binding Model
• Diagnostics of Hilbert space fragmentation, freezing transition, and its effects in the family of quantum East models involving varying range of constraints
• Statistics of noninteracting many-body fermionic states: The question of a many-body mobility edge
• PT -symmetry breaking and universal spectral statistics in quantum kicked rotors
• Energy dynamics in a class of local random matrix Hamiltonians
• Relaxation Fluctuations of Correlation Functions: Spin and Random Matrix Models
• Reciprocal Floquet thermalization in one-dimensional Rydberg atom array
• Loss of integrability in a system with two-photon interactions
• Bridging Classical and Quantum Information Scrambling with the Operator Entanglement Spectrum
• Haldane graphene billiards versus relativistic neutrino billiards
• Circular Rosenzweig-Porter random matrix ensemble
• Edge of Many-Body Quantum Chaos in Quantum Reservoir Computing
• Holographic nature of critical quantum states of proteins
• Estimating time in quantum chaotic systems and black holes
• Matter Coupling of Dirac Matter in the Context of the SYK Model: Non-Gaussian Random Couplings and Bulk Mass Deformations
• Dynamic thermalization on noisy quantum hardware
• Exponential $U(1)$ Symmetry-Breaking Phase as a Disorder-Free Quantum Glass
• Statistical properties of mutualistic-competitive random networks
• Nonlocality, Integrability and Quantum Chaos in the Spectrum of Bell Operators
• Spectral properties of three-dimensional Anderson model
• Anomalous transport in U(1)-symmetric quantum circuits
• Practical Quantum Reservoir Computing in Rydberg Atom Arrays
• Crossover from Quantum Chaos to a Reversed Quantum Disentangled Liquid in a Disorder-Free Spin Ladder
• Long term behavior of the stirred vacuum on a Dirac chain: geometry blur and the random Slater ensemble
• Observation of strong and weak thermalization in a superconducting quantum processor
• Imprints of $U_A(1)$ chiral anomaly and disorder in the Dirac eigenspectrum of QCD at finite temperature
• Limitations of SVD-Based Diagnostics for Non-Hermitian Many-Body Localization with Time-Reversal Symmetry
• Comparative Study of Indicators of Chaos in the Closed and Open Dicke Model
• Measurement-Induced Dynamical Quantum Thermalization
• Effects of critical correlations on quantum percolation in two dimensions
• Probing the randomness of ergodic states: extreme-value statistics in the ergodic and many-body-localized phases
• Effects of dilution in a 2D topological magnon insulator
• Euclidean-to-Lorentzian wormhole transition and gravitational symmetry breaking in the Sachdev-Ye-Kitaev model
• Generalized Calogero-Sutherland models for Kondo physics in the Luttinger liquid
• Probing the localization effects in Krylov basis
• Relaxation mechanisms in a disordered system with the Poisson level statistics
• Localization transitions in quadratic systems without quantum chaos
• Rationally independent free fermions with local hopping
• Localization and fractality in disordered Russian Doll model
• Information acquisition, scrambling, and sensitivity to errors in quantum chaos
• Certain BCS wavefunctions are quantum many-body scars
• Universal transition of spectral fluctuation in particle-hole symmetric system
• A sharp transition in quantum chaos and thermodynamics of mass deformed SYK model
• Universal Relation between Spectral and Wavefunction Properties at Criticality
• Unsupervised Techniques to Detect Quantum Chaos
• Quantum many-body scarring from Kramers-Wannier duality
• Many-body localization and particle multioccupancy in the disordered Bose-Hubbard model
• Statistics-encoded tensor network approach in disordered quantum many-body spin chains
• Entanglement dynamics and ergodicity breaking in a quantum cellular automaton
• Disorder, Low-Energy Excitations, and Topology in the Kitaev Spin Liquid
• Nonergodic dynamics of the one-dimensional Bose-Hubbard model with a trapping potential
• Chaos assisted many-body tunnelling
• Disordered statistical physics in low dimensions: extremes, glass transition, and localization
• Equilibration of Non-interacting Photons and Quantum Signatures of Chaos
• Spectral statistics and energy-gap scaling in $k-$local spin Hamiltonians
• A bipartite Sachdev-Ye-Kitaev model: Conformal limit and level statistics
• Quantum Avalanches in ${\mathbb{Z}}_2$-preserving Interacting Ising Majorana Chain
• Exploring the properties of quantum scars in a toy model
• Supercell symmetry modified spectral statistics of Kramers-Weyl fermions
• Dissipative quantum dynamics, phase transitions and non-Hermitian random matrices
• From Bell Products to Greenberger-Horne-Zeilinger states: Quantum Memories via emergent Hamiltonians
• Quantum Lyapunov exponents and complex spacing ratios: two measures of Dissipative Quantum Chaos
• Stable infinite-temperature eigenstates in SU(2)-symmetric nonintegrable models
• Emergent Thermalization Thresholds in Unitary Dynamics of Inhomogeneously Disordered Quantum Systems
• Entanglement Growth from Entangled States: A Unified Perspective on Entanglement Generation and Transport
• Additional quantum many-body scars of the spin-$1$ $XY$ model with Fock-space cages and commutant algebras
• Quantum transitions, ergodicity, and quantum scars in the coupled top model
• From single-particle to many-body chaos in Yukawa--SYK: theory and a cavity-QED proposal
• On a Matrix Ensemble for Arbitrary Complex Quantum Systems
• Surmise for random matrices' level spacing distributions beyond nearest-neighbors
• Floquet thermalization by power-law induced permutation symmetry breaking
• Momentum-space modulated symmetries in the Luttinger liquid
• Higher-Order Krylov State Complexity in Random Matrix Quenches
• Floquet Recurrences in the Double Kicked Top
• Bosonic near-CFT${}_1$ models from Fock-space fluxes
• Transport scaling and critical tilt effects in disordered two-dimensional Dirac fermions
• Distinct many-body scars and emergent quantum phases driven by competing interactions in two-species Rydberg arrays
• Crystalline Spectral Form Factors
• Dynamical irreversibility and local decoherence in quantum many-body chaos