Related papers: Eigenvalue Distributions of the QCD Dirac Operator

In a deep-infrared (ergodic) regime, QCD coupled to massive pseudoreal and real quarks are described by chiral orthogonal and symplectic ensembles of random matrices. Using this correspondence, general expressions for the QCD partition…

In the epsilon-regime of lattice QCD one can get an accurate measurement of the pion decay constant F_pi by monitoring how just one single Dirac operator eigenvalue splits into two when subjected to two different external vector sources.…

In this lecture we review recent lattice QCD studies of the statistical properties of the eigenvalues of the QCD Dirac operator. We find that the fluctuations of the smallest Dirac eigenvalues are described by chiral Random Matrix Theories…

In the presence of a non-vanishing chemical potential the eigenvalues of the Dirac operator become complex. We calculate spectral correlation functions of complex eigenvalues using a random matrix model approach. Our results apply to…

We investigate the eigenvalues and eigenvectors of the staggered Dirac operator in the vicinity of the chiral phase transition of quenched SU(3) lattice gauge theory. We consider both the global features of the spectrum and the local…

We summarize the analytical solution of the Chiral Perturbation Theory for the Hermitian Wilson Dirac operator of $N_c=2$ QCD with quarks in the fundamental representation. Results have been obtained for the quenched microscopic spectral…

We discuss some properties of zero and near-zero modes of the Dirac operator, as observed in a recent simulation of 2-flavor QCD. The quarks have been implemented with the so-called Chirally Improved Dirac operator, which obeys the…

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…

We calculate numerically the eigenvalue distribution of the overlap Dirac operator in the quenched Schwinger model on a lattice. The distribution does not fit any of the three universality classes of spontaneous chiral symmetry breaking,…

The microscopic spectral eigenvalue correlations of QCD Dirac operators in the presence of dynamical fermions are calculated within the framework of Random Matrix Theory (RMT). Our approach treats the low--energy correlation functions of…

We investigate the spectral properties of the Wilson Dirac operator in quenched QCD in the microscopic regime. We distinguish the topological sectors using the index as determined by the Wilson flow method. Consequently, the distributions…

We investigate the eigenvalue spectrum of the staggered Dirac matrix in two color QCD at finite chemical potential. The profiles of complex eigenvalues close to the origin are compared to a complex generalization of the chiral Gaussian…

All microscopic correlation functions of the spectrum of the Hermitian Wilson Dirac operator with any number of flavors with equal masses are computed. In particular, we give explicit results for the spectral density in the physical case…

We utilize the eigenvalue filtering technique combined with the stochastic estimate of the mode number to determine the eigenvalue spectrum. Simulations of (2 + 1)-flavor QCD are performed using the Highly Improved Staggered Quarks…

We consider the spectrum of the staggered Dirac operator with SU(2) gauge fields. Our study is motivated by the fact that the antiunitary symmetries of this operator are different from those of the SU(2) continuum Dirac operator. In this…

Dirac operator eigenvalues split into two when subjected to two different external vector sources. In a specific finite-volume scaling regime of gauge theories with fermions, this problem can be mapped to a chiral Random Two-Matrix Theory.…

We study some interesting aspects of the spectral properties of SU(3) gauge theory, both with and without dynamical quarks (QCD) at thermal equilibrium using lattice gauge theory techniques. By calculating the eigenstates of a massless…

We investigate the eigenvalue spectrum of the staggered Dirac matrix in two-color QCD at nonzero temperature and at baryon density when the eigenvalues become complex. The quasi-zero modes and their role for chiral symmetry breaking and the…

We compare eigenvalue correlations of the Dirac operator with a chemical potential obtained from lattice simulations of quenched QCD with analytic predictions obtained from chiral effective theories in the zero-momentum limit. By comparing…

We have constructed the lowest few eigenvectors of the staggered Dirac operator on SU(3) gauge configurations, both quenched and dynamical. We use these modes to study the topological charge and to construct approximate hadronic…