Dirac eigenvalue correlations in quenched QCD at finite density

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 the density and two-point correlation function we show that the analytic results agree with QCD at low energies. We also examine the scale (Thouless energy) up to which the zero-momentum approximation is valid.Comment: 6 pages, 12 figures, talk given at Lattice 200

Staggered chiral random matrix theory

We present a random matrix theory (RMT) for the staggered lattice QCD Dirac operator. The staggered RMT is equivalent to the zero-momentum limit of the staggered chiral Lagrangian and includes all taste breaking terms at their leading order. This is an extension of previous work which only included some of the taste breaking terms. We will also present some results for the taste breaking contributions to the partition function and the Dirac eigenvalues.Comment: 12 pages, 7 figures, v2 has minor edits and corrections to some equations to match published versio

Eigenvalue correlations in QCD with a chemical potential

We discuss a new Random Matrix Model for QCD with a chemical potential that is based on the symmetries of the Dirac operator and can be solved exactly for all eigenvalue correlations for any number of flavors. In the microscopic limit of small energy levels the results should be an accurate description of QCD. This new model can also be scaled so that all physical observables remain at their $\mu=0$ values until a first order chiral restoration transition is reached. This gives a more realistic model for the QCD phase diagram than previous RMM. We also mention how the model might aid in determining the phase diagram of QCD from future numerical simulations.Comment: 3 pages, 3 figures, Lattice2004(non-zero

The QCD vacuum as a disordered medium: A simplified model for the QCD Dirac operator

We model the QCD Dirac operator as a power-law random banded matrix (RBM) with the appropriate chiral symmetry. Our motivation is the form of the Dirac operator in a basis of instantonic zero modes with a corresponding gauge background of instantons. We compare the spectral correlations of this model to those of an instanton liquid model (ILM) and find agreement well beyond the Thouless energy. In the bulk of the spectrum the (dimensionless) Thouless energy of the RBM scales with the square root of system size in agreement with the ILM and chiral perturbation theory. Near the origin the scaling of the (dimensionless) Thouless energy in the RBM remains the same as in the bulk which agrees with chiral perturbation theory but not with the ILM. Finally we discuss how this RBM should be modified in order to describe the spectral correlations of the QCD Dirac operator at the finite temperature chiral restoration transition.Comment: 4 pages, 3 figure