Chiral Condensate at Nonzero Chemical Potential in the Microscopic Limit of QCD

Abstract

The chiral condensate in QCD at zero temperature does not depend on the quark chemical potential (up to one third the nucleon mass), whereas the spectral density of the Dirac operator shows a strong dependence on the chemical potential. The cancellations which make this possible also occur on the microscopic scale, where they can be investigated by means of a random matrix model. We show that they can be understood in terms of orthogonality properties of orthogonal polynomials. In the strong non-Hermiticity limit they are related to integrability properties of the spectral density. As a by-product we find exact analytical expressions for the partially quenched chiral condensate in the microscopic domain at nonzero chemical potential.

29 pages, 5 figures, version to appear in PRD

References in corpus (5)

• The QCD Sign Problem for Small Chemical Potential
• QCD in One Dimension at Nonzero Chemical Potential
• QCD with Bosonic Quarks at Nonzero Chemical Potential
• Phase Diagram of the Dirac Spectrum at Nonzero Chemical Potential
• Equivalence of Matrix Models for Complex QCD Dirac Spectra

Cited by in corpus (8)

• Full simulation of chiral Random Matrix Theory at non-zero chemical potential by Complex Langevin
• Dense QCD in a Finite Volume
• Random matrix analysis of the QCD sign problem for general topology
• The Dirac spectrum in Complex Langevin Simulations of QCD
• Phase Diagram of the Dirac Spectrum at Nonzero Chemical Potential
• Subsets and the canonical partition functions
• Handbook Article on Applications of Random Matrix Theory to QCD
• Banks-Casher-type relations for complex Dirac spectra