Chiral Random Matrix Model at Finite Chemical Potential: Characteristic Determinant and Edge Universality
arXiv:1602.02578 · doi:10.1016/j.nuclphysb.2016.04.040
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.
16 pages, 4 figures
References in corpus (7)
- The QCD Sign Problem for Small Chemical Potential
- Full simulation of chiral Random Matrix Theory at non-zero chemical potential by Complex Langevin
- Dysonian dynamics of the Ginibre ensemble
- A Random Matrix Study of the QCD Sign Problem
- Unveiling the significance of eigenvectors in diffusing non-hermitian matrices by identifying the underlying Burgers dynamics
- Hydrodynamical spectral evolution for random matrices
- Random matrix model at nonzero chemical potentials with anomaly effects