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

Takuya Kanazawa (Research and Development Group, Hitachi, Ltd., Kokubunji, Tokyo 185-8601, Japan) ; Mario Kieburg (Fakultät für Physik, Universität Bielefeld, 33501 Bielefeld, Germany)

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 a 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 $ϵ$ regime of QCD. We compare these analytical results with Monte Carlo simulations of the matrix model.

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Published on:
11 June 2018
Publisher:
APS
Published in:
Physical Review Letters , Volume 120 (2018)
Issue 24
DOI:
https://doi.org/10.1103/PhysRevLett.120.242001
arXiv:
1803.04122