Universality crossover between chiral random matrix ensembles and twisted SU(2) lattice Dirac spectra

Abstract

Motivated by the statistical fluctuation of Dirac spectrum of QCD-like theories subjected to (pseudo)reality-violating perturbations and in the epsilon-regime, we compute the smallest eigenvalue distribution and the level spacing distribution of chiral and non-chiral parametric random matrix ensembles of Dyson-Mehta-Pandey type. To this end we employ the Nystrom method to numerically evaluate the Fredholm Pfaffian of the integral kernel for the chG(O,S)E-chGUE and G(O,S)E-GUE crossover. We confirm the validity and universality of our results by comparing them with several lattice models, namely fundamental and adjoint staggered Dirac spectra of SU(2) quenched lattice gauge theory under the twisted boundary condition (imaginary chemical potential) or perturbed by phase noise. Both in the zero-virtuality region and in the spectral bulk, excellent one-parameter fitting is achieved already on a small 4^4 lattice. Anticipated scaling of the fitting parameter with the twisting phase, mean level spacing, and the system size allows for precise determination of the pion decay (diffusion) constant F in the low-energy effective Lagrangian.

18 pages in REVTeX, 30 figures. (v2) 40000 configurations used for all parameter sets, statistical errors included in all quantities, erroneous chi^2/dof corrected. (v3) Version to appear in Phys. Rev. D86 (2012)

References in corpus (11)

• Electromagnetic mass splittings of the low lying hadrons and quark masses from 2+1 flavor lattice QCD+QED
• Matrix Models and QCD with Chemical Potential
• Overlap Dirac operator at nonzero chemical potential and random matrix theory
• A new Chiral Two-Matrix Theory for Dirac Spectra with Imaginary Chemical Potential
• Microscopic eigenvalue correlations in QCD with imaginary isospin chemical potential
• Extracting $F_{\pi }$ from small lattices: unquenched results
• Unquenched complex Dirac spectra at nonzero chemical potential: two-colour QCD lattice data versus matrix model
• Semiclassical Theory for Parametric Correlation of Energy Levels
• Geometry dependence of RMT-based methods to extract the low-energy constants Sigma and F
• Semiclassical Approach to Parametric Spectral Correlation with Spin 1/2
• Level spacings for weakly asymmetric real random matrices and application to two-color QCD with chemical potential

Cited by in corpus (5)

• Poisson to Random Matrix Transition in the QCD Dirac Spectrum
• Completing the picture for the smallest eigenvalue of real Wishart matrices
• Statistical properties of eigenvalues of the non-Hermitian Su-Schrieffer-Heeger model with random hopping terms
• Preserving Topology while Breaking Chirality: From Chiral Orthogonal to Anti-symmetric Hermitian Ensemble
• Accuracy and range of validity of the Wigner surmise for mixed symmetry classes in random matrix theory