A Wigner Surmise for Hermitian and Non-Hermitian Chiral Random Matrices

Abstract

We use the idea of a Wigner surmise to compute approximate distributions of the first eigenvalue in chiral Random Matrix Theory, for both real and complex eigenvalues. Testing against known results for zero and maximal non-Hermiticity in the microscopic large-N limit we find an excellent agreement, valid for a small number of exact zero-eigenvalues. New compact expressions are derived for real eigenvalues in the orthogonal and symplectic classes, and at intermediate non-Hermiticity for the unitary and symplectic classes. Such individual Dirac eigenvalue distributions are a useful tool in Lattice Gauge Theory and we illustrate this by showing that our new results can describe data from two-colour QCD simulations with chemical potential in the symplectic class.

4 pages, 5 figures

References in corpus (8)

• Phase of the Fermion Determinant at Nonzero Chemical Potential
• The QCD Sign Problem for Small Chemical Potential
• The Complex Laguerre Symplectic Ensemble of Non-Hermitian Matrices
• Overlap Dirac operator at nonzero chemical potential and random matrix theory
• Gap Probabilities in Non-Hermitian Random Matrix Theory
• Unquenched complex Dirac spectra at nonzero chemical potential: two-colour QCD lattice data versus matrix model
• Individual complex Dirac eigenvalue distributions from random matrix theory and comparison to quenched lattice QCD with a quark chemical potential
• Finite-temperature chiral condensate and low-lying Dirac eigenvalues in quenched SU(2) lattice gauge theory

Cited by in corpus (16)

• Symmetry Classification and Universality in Non-Hermitian Many-Body Quantum Chaos by the Sachdev-Ye-Kitaev Model
• Symmetry Classification of Many-Body Lindbladians: Tenfold Way and Beyond
• Wigner surmise for mixed symmetry classes in random matrix theory
• Universal distribution of Lyapunov exponents for products of Ginibre matrices
• Periodic Table of SYK and supersymmetric SYK
• Compact smallest eigenvalue expressions in Wishart-Laguerre ensembles with or without fixed-trace
• Mixing of orthogonal and skew-orthogonal polynomials and its relation to Wilson RMT
• Statistical properties of eigenvalues of the non-Hermitian Su-Schrieffer-Heeger model with random hopping terms
• Spacing distribution in the 2D Coulomb gas: Surmise and symmetry classes of non-Hermitian random matrices at non-integer $\beta$
• Field theory of non-Hermitian disordered systems
• Random matrix model for QCD_3 staggered fermions
• Universality crossover between chiral random matrix ensembles and twisted SU(2) lattice Dirac spectra
• Universal hard-edge statistics of non-Hermitian random matrices
• Level spacings for weakly asymmetric real random matrices and application to two-color QCD with chemical potential
• Sixfold Way of Traversable Wormholes in the Sachdev-Ye-Kitaev Model
• Accuracy and range of validity of the Wigner surmise for mixed symmetry classes in random matrix theory