Random Matrix Theory for the Hermitian Wilson Dirac Operator and the chGUE-GUE Transition

Abstract

We introduce a random two-matrix model interpolating between a chiral Hermitian (2n+nu)x(2n+nu) matrix and a second Hermitian matrix without symmetries. These are taken from the chiral Gaussian Unitary Ensemble (chGUE) and Gaussian Unitary Ensemble (GUE), respectively. In the microscopic large-n limit in the vicinity of the chGUE (which we denote by weakly non-chiral limit) this theory is in one to one correspondence to the partition function of Wilson chiral perturbation theory in the epsilon regime, such as the related two matrix-model previously introduced in refs. [20,21]. For a generic number of flavours and rectangular block matrices in the chGUE part we derive an eigenvalue representation for the partition function displaying a Pfaffian structure. In the quenched case with nu=0,1 we derive all spectral correlations functions in our model for finite-n, given in terms of skew-orthogonal polynomials. The latter are expressed as Gaussian integrals over standard Laguerre polynomials. In the weakly non-chiral microscopic limit this yields all corresponding quenched eigenvalue correlation functions of the Hermitian Wilson operator.

27 pages, 4 figures; v2 typos corrected, published version

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Cited by in corpus (30)

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• Finite-Volume Scaling of the Wilson-Dirac Operator Spectrum
• Phase Diagram of Dynamical Twisted Mass Wilson Fermions at Finite Isospin Chemical Potential
• Determination of Low-Energy Constants of Wilson Chiral Perturbation Theory
• Spectral Properties of the Wilson Dirac Operator and random matrix theory
• The Realization of the Sharpe-Singleton Scenario
• Mixing of orthogonal and skew-orthogonal polynomials and its relation to Wilson RMT
• New Ways to Determine Low-Energy Constants with Wilson Fermions
• Random Matrix Theory and Quantum Chromodynamics
• Dirac Spectrum of the Wilson Dirac Operator for QCD with Two Colors
• GUE-chGUE Transition preserving Chirality at finite Matrix Size
• Toward a classification of PT-symmetric quantum systems: From dissipative dynamics to topology and wormholes
• Symmetry Transition Preserving Chirality in QCD: A Versatile Random Matrix Model
• Supersymmetry Method for Chiral Random Matrix Theory with Arbitrary Rotation Invariant Weights
• Individual Eigenvalue Distributions for the Wilson Dirac Operator
• Symmetry Crossover Protecting Chirality in Dirac Spectra
• Chiral Dynamics With Wilson Fermions
• Microscopic Spectral Density of the Wilson Dirac Operator for One Flavor
• Random Matrix Models for Dirac Operators at finite Lattice Spacing
• Emergent Topology in Many-Body Dissipative Quantum Matter
• Consecutive level spacings in the chiral Gaussian unitary ensemble: From the hard and soft edge to the bulk
• Progress on the Microscopic Spectrum of the Dirac Operator for QCD with Wilson Fermions
• Wilson chiral perturbation theory, Wilson-Dirac operator eigenvalues and clover improvement
• Chiral random matrix theory for colorful quark-antiquark condensates
• Random Matrix Models for the Hermitian Wilson-Dirac operator of QCD-like theories
• Exploring the Aoki regime
• Preserving Topology while Breaking Chirality: From Chiral Orthogonal to Anti-symmetric Hermitian Ensemble
• Universal Broadening of Zero Modes: A General Framework and Identification
• Singular Value Statistics for the Spiked Elliptic Ginibre Ensemble