Unquenched complex Dirac spectra at nonzero chemical potential: two-colour QCD lattice data versus matrix model

Abstract

We compare analytic predictions of non-Hermitian chiral random matrix theory with the complex Dirac operator eigenvalue spectrum of two-colour lattice gauge theory with dynamical fermions at nonzero chemical potential. The Dirac eigenvalues come in complex conjugate pairs, making the action of this theory real, and positive for our choice of two staggered flavours. This enables us to use standard Monte-Carlo in testing the influence of chemical potential and quark mass on complex eigenvalues close to the origin. We find an excellent agreement between the analytic predictions and our data for two different volumes over a range of chemical potentials below the chiral phase transition. In particular we detect the effect of unquenching when going to very small quark masses.

4 pages, 6 figures; v2: grant no. added

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• Chiral Lagrangian and spectral sum rules for dense two-color QCD
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• Massive partition functions and complex eigenvalue correlations in Matrix Models with symplectic symmetry
• A Wigner Surmise for Hermitian and Non-Hermitian Chiral Random Matrices
• Skew-orthogonal polynomials in the complex plane and their Bergman-like kernels
• Statistical properties of eigenvalues of the non-Hermitian Su-Schrieffer-Heeger model with random hopping terms
• Universal eigenvector correlations in quaternionic Ginibre ensembles
• Scaling Limits of Planar Symplectic Ensembles
• Universality crossover between chiral random matrix ensembles and twisted SU(2) lattice Dirac spectra