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

TL;DR

This paper derives a novel relation connecting the density of Dirac eigenvalues at zero to the BCS gap in high-density QCD-like theories, enabling lattice measurement of the gap.

Contribution

It introduces a Banks-Casher-type relation for the BCS gap applicable to sign-problem-free QCD-like theories, linking spectral density to the gap.

Findings

Derivation of a new relation between Dirac eigenvalues and the BCS gap.

Applicability to QCD, two-color QCD, and QCD with isospin chemical potential.

Provides a lattice method to measure the BCS gap.

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.