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.

arXiv comment29 pages, 5 figures, version to appear in PRD

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Cited by in corpus (21)

• Introductory lectures on lattice QCD at nonzero baryon number
• Complex Langevin Dynamics for chiral Random Matrix Theory
• Singular values of the Dirac operator in dense QCD-like theories
• 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
• Random matrix theory of unquenched two-colour QCD with nonzero chemical potential
• Distributions of the Phase Angle of the Fermion Determinant in QCD
• The Dirac spectrum in Complex Langevin Simulations of QCD
• Evading the sign problem in random matrix simulations
• Mixing of orthogonal and skew-orthogonal polynomials and its relation to Wilson RMT
• Phase Diagram of the Dirac Spectrum at Nonzero Chemical Potential
• Subsets and the canonical partition functions
• The QCD sign problem as a total derivative
• Banks-Casher-type relation for the BCS gap at high density
• Baryon Number Dirac Spectrum in QCD
• A subset solution to the sign problem in random matrix simulations
• Handbook Article on Applications of Random Matrix Theory to QCD
• Lessons from Random Matrix Theory for QCD at Finite Density
• The Fluctuations of the Quark Number and of the Chiral Condensate
• Banks-Casher-type relations for complex Dirac spectra