Phase Diagram of the Dirac Spectrum at Nonzero Chemical Potential

Abstract

The Dirac spectrum of QCD with dynamical fermions at nonzero chemical potential is characterized by three regions, a region with a constant eigenvalue density, a region where the eigenvalue density shows oscillations that grow exponentially with the volume and the remainder of the complex plane where the eigenvalue density is zero. In this paper we derive the phase diagram of the Dirac spectrum from a chiral Lagrangian. We show that the constant eigenvalue density corresponds to a pion condensed phase while the strongly oscillating region is given by a kaon condensed phase. The normal phase with nonzero chiral condensate but vanishing Bose condensates coincides with the region of the complex plane where there are no eigenvalues.

17 pages, 3 figures

References in corpus (26)

• QCD at finite isospin density
• Random matrix theory and spectral sum rules for the Dirac operator in QCD
• The spectrum of the QCD Dirac operator and chiral random matrix theory: the threefold way
• Random matrix model of QCD at finite density and the nature of the quenched limit
• Functional integrals for QCD at nonzero chemical potential and zero density
• Universal results from an alternate random matrix model for QCD with a baryon chemical potential
• Non-Hermitian Random Matrix Theory and Lattice QCD with Chemical Potential
• Factorization of Correlation Functions and the Replica Limit of the Toda Lattice Equation
• Unquenched QCD Dirac Operator Spectra at Nonzero Baryon Chemical Potential
• Diquark Condensate in QCD with Two Colors at Next-to-Leading Order
• Chiral Symmetry Breaking and the Dirac Spectrum at Nonzero Chemical Potential
• Universal scaling of the valence quark mass dependence of the chiral condensate
• Thermodynamics of chiral symmetry at low densities
• Replica Limit of the Toda Lattice Equation
• Replica field theories, Painleve transcendents, and exact correlation functions
• Effective Low Energy Theories and QCD Dirac Spectra
• The QCD phase diagram at nonzero baryon, isospin and strangeness chemical potentials: Results from a hadron resonance gas model
• QCD Dirac operator at nonzero chemical potential: lattice data and matrix model
• Chiral Condensate at Nonzero Chemical Potential in the Microscopic Limit of QCD
• Instantons and the Chiral Phase Transition at non-zero Baryon Density
• Pathologies of Quenched Lattice QCD at non--zero Density and its Effective Potential
• Individual complex Dirac eigenvalue distributions from random matrix theory and comparison to quenched lattice QCD with a quark chemical potential
• 3D two-color QCD at finite temperature and baryon density
• Individual Eigenvalue Distributions of Chiral Random Two-Matrix Theory and the Determination of F_pi
• Quantum chaos in supersymmetric QCD at finite density
• Chiral Symmetry Breaking at Nonzero Chemical Potential

Cited by in corpus (13)

• Random matrix theory of unquenched two-colour QCD with nonzero chemical potential
• Chiral Condensate at Nonzero Chemical Potential in the Microscopic Limit of QCD
• Distributions of the Phase Angle of the Fermion Determinant in QCD
• The Dirac spectrum in Complex Langevin Simulations of QCD
• The Realization of the Sharpe-Singleton Scenario
• Mixing of orthogonal and skew-orthogonal polynomials and its relation to Wilson RMT
• Subsets and the canonical partition functions
• Banks-Casher-type relation for the BCS gap at high density
• Baryon Number Dirac Spectrum in QCD
• Handbook Article on Applications of Random Matrix Theory to QCD
• Random matrix models for phase diagrams
• The Fluctuations of the Quark Number and of the Chiral Condensate
• The interplay of the sign problem and the infinite volume limit: gauge theories with a theta term