Chiral Random Matrix Model at Finite Chemical Potential: Characteristic Determinant and Edge Universality

TL;DR

This paper develops an exact formula for the evolution of the characteristic determinant in a chiral random matrix model at finite chemical potential, revealing universal edge behaviors that can inform lattice QCD analyses.

Contribution

It introduces a novel exact formula for the characteristic determinant's evolution and demonstrates its universal edge properties at finite chemical potential.

Findings

Universal edge functions describe eigenvalue droplet boundaries.

Chiral condensate can be extracted from lattice spectra using universal laws.

Exact stochastic evolution formula derived for deformed Wishart matrices.

Abstract

We derive an exact formula for the stochastic evolution of the characteristic determinant of a class of deformed Wishart matrices following from a chiral random matrix model of QCD at finite chemical potential. In the WKB approximation, the characteristic determinant describes a sharp droplet of eigenvalues that deforms and expands at large stochastic times. Beyond the WKB limit, the edges of the droplet are fuzzy and described by universal edge functions. At the chiral point, the characteristic determinant in the microscopic limit is universal. Remarkably, the physical chiral condensate at finite chemical potential may be extracted from current and quenched lattice Dirac spectra using the universal edge scaling laws, without having to solve the QCD sign problem.