Universal scaling of higher-order spacing ratios in Gaussian random matrices

Abstract

Higher-order spacing ratios are investigated analytically using a Wigner-like surmise for Gaussian ensembles of random matrices. For $k$-th order spacing ratio $(r^{(k)}$, $k>1)$ the matrix of dimension $2k+1$ is considered. A universal scaling relation for this ratio, known from earlier numerical studies, is proved in the asymptotic limits of $r^{(k)}\to 0$ and $r^{(k)}\to \infty$.

arXiv comment12 pages. This is a substantially improved version. Accepted for publication in Physical Review E. Comments are welcome

References in corpus (51)

• Random Matrix Theories in Quantum Physics: Common Concepts
• Localization of interacting fermions at high temperature
• The many-body localization phase transition
• The distribution of the ratio of consecutive level spacings in random matrix ensembles
• A Random Matrix Approach to Cross-Correlations in Financial Data
• Black Holes and Random Matrices
• Matrix Models for Beta Ensembles
• The spectrum of the QCD Dirac operator and chiral random matrix theory: the threefold way
• Many-Body Localization in a Quasiperiodic System
• Random Matrix Theory and Chiral Symmetry in QCD
• Random-matrix theory of Majorana fermions and topological superconductors
• Complex Spacing Ratios: A Signature of Dissipative Quantum Chaos
• Large Deviations of the Maximum Eigenvalue for Wishart and Gaussian Random Matrices
• Misleading signatures of quantum chaos
• Energy transport in disordered classical spin chains
• The spectrum of the Dirac operator near zero virtuality for $N_c=2$
• Level statistics across the many--body localization transition
• Universality classes of the Anderson Transitions Driven by non-Hermitian Disorder
• Joint probability densities of level spacing ratios in random matrices
• Random matrix analysis of complex networks
• Model of level statistics for disordered interacting quantum many-body systems
• Random Matrix Ensemble for the Level Statistics of Many-Body Localization
• Level statistics of disordered spin-1/2 systems and its implications for materials with localized Cooper pairs
• Higher order spacing ratios in random matrix theory and complex quantum systems
• Thouless Energy and Correlations of QCD Dirac Eigenvalues
• Poisson to GOE transition in the distribution of the ratio of consecutive level spacings
• Spectral transitions and universal steady states in random Kraus maps and circuits
• Energy level statistics of the two-dimensional Hubbard model at low filling
• Periodic Table of SYK and supersymmetric SYK
• Higher-order level spacings in random matrix theory based on Wigner's conjecture
• Signatures of Chaos in Non-integrable Models of Quantum Field Theory
• On correlation functions of characteristic polynomials for chiral Gaussian Unitary Ensemble
• A random matrix decimation procedure relating $\beta =2/(r+1)$ to $\beta =2(r+1)$
• Exact distribution of spacing ratios for random and localized states in quantum chaotic systems
• A microwave realization of the chiral orthogonal, unitary, and symplectic ensembles
• Symmetry deduction from spectral fluctuations in complex quantum systems
• Scaling in the eigenvalue fluctuations of the empirical correlation matrices
• $Q$-Laguerre spectral density and quantum chaos in the Wishart-Sachdev-Ye-Kitaev model
• Superposition and higher-order spacing ratios in random matrix theory with application to complex systems
• Approximation formula for complex spacing ratios in the Ginibre ensemble
• Critical Level Statistics at the Many-Body Localization Transition Region
• Classification of the quantum chaos in colored Sachdev-Ye-Kitaev models
• Supersymmetry Method for Chiral Random Matrix Theory with Arbitrary Rotation Invariant Weights
• Chiral Random Matrix Theory and Chiral Perturbation Theory
• Spectral Crossovers and Universality in Quantum Spin-chains Coupled to Random Fields
• On intermediate statistics across many-body localization transition
• Spectral statistics of multi-parametric Gaussian ensembles with chiral symmetry
• Random matrix theory and critical phenomena in quantum spin chains
• Random Matrix Model for Eigenvalue Statistics in Random Spin Systems
• Consecutive level spacings in the chiral Gaussian unitary ensemble: From the hard and soft edge to the bulk
• Dissipative quantum dynamics, phase transitions and non-Hermitian random matrices

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