Banks-Casher-type relation for the BCS gap at high density

Abstract

We derive a new Banks-Casher-type relation which relates the density of complex Dirac eigenvalues at the origin to the BCS gap of quarks at high density. Our relation is applicable to QCD and QCD-like theories without a sign problem, such as two-color QCD and adjoint QCD with baryon chemical potential, and QCD with isospin chemical potential. It provides us with a method to measure the BCS gap through the Dirac spectrum on the lattice.

14 pages, 2 figures, some additions (in particular eq. (4.13)), version to appear in EPJA

References in corpus (12)

• Color superconductivity in dense quark matter
• Chiral symmetry breaking and the Banks--Casher relation in lattice QCD with Wilson quarks
• Universality of Phases in QCD and QCD-like Theories
• Singular values of the Dirac operator in dense QCD-like theories
• Universal Aspects of QCD-like Theories
• Matrix Models and QCD with Chemical Potential
• Chiral Lagrangian and spectral sum rules for dense two-color QCD
• Dense QCD in a Finite Volume
• Chiral Condensate at Nonzero Chemical Potential in the Microscopic Limit of QCD
• QCD with Bosonic Quarks at Nonzero Chemical Potential
• Phase Diagram of the Dirac Spectrum at Nonzero Chemical Potential
• The QCD Phase Transition Region with Domain Wall Quarks

Cited by in corpus (8)

• Study of the phase diagram of dense two-color QCD within lattice simulation
• Two-colour QCD phases and the topology at low temperature and high density
• Stressed Cooper pairing in QCD at high isospin density: effective Lagrangian and random matrix theory
• Chiral symmetry breaking with no bilinear condensate revisited
• Classification of the quantum chaos in colored Sachdev-Ye-Kitaev models
• Finite-Density Massless Two-Color QCD at Isospin Roberge-Weiss Point and 't Hooft Anomaly
• Chiral random matrix theory for single-flavor spin-one Cooper pairing
• Relativistic Cooper pairing in the microscopic limit of chiral random matrix theory