Symmetry Transition Preserving Chirality in QCD: A Versatile Random Matrix Model

Abstract

We consider a random matrix model which interpolates between the chiral Gaussian unitary ensemble and the Gaussian unitary ensemble while preserving chiral symmetry. This ensemble describes flavor symmetry breaking for staggered fermions in 3d QCD as well as in 4d QCD at high temperature or in 3d QCD at finite isospin chemical potential. Our model is an Osborn-type two-matrix model which is equivalent to the elliptic ensemble but we consider the singular value statistics rather than the complex eigenvalue statistics. We report on exact results for the partition function and the microscopic level density of the Dirac operator in the $\epsilon$-regime of QCD. We compare these analytical results with Monte Carlo simulations of the matrix model.

5 pages, 1 figure, PACS numbers: 02.10.Yn,05.50.+q,11.15.Ex,11.15.Ha,12.38.-t

References in corpus (8)

• Dirac materials
• Superbosonization of invariant random matrix ensembles
• Matrix Models and QCD with Chemical Potential
• Comparison of the superbosonization formula and the generalized Hubbard-Stratonovich transformation
• GUE-chGUE Transition preserving Chirality at finite Matrix Size
• Random matrix model for QCD_3 staggered fermions
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• Symmetry Crossover Protecting Chirality in Dirac Spectra
• Spectral and Strength Statistics of Chiral Brownian Ensemble
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• Universal Broadening of Zero Modes: A General Framework and Identification
• Preserving Topology while Breaking Chirality: From Chiral Orthogonal to Anti-symmetric Hermitian Ensemble
• Singular Value Statistics for the Spiked Elliptic Ginibre Ensemble