D. K. Sinclair, J.-F. Lagaë, and G. T. Bodwin,
Argonne National Laboratory
J. B. Kogut, University of Illinois

Research Objectives

One problem which complicates lattice QCD simulations with the standard staggered or Wilson methods of putting quarks on the lattice is that chiral flavor symmetry is explicitly broken by these discretizations. Defining the quarks on a 5-dimensional lattice with open boundary conditions in the fifth dimension yields a lattice transcription whose 4-dimensional projection is explicitly chiral, but only when the lattice extent in the fifth dimension (N₅) becomes infinite. The question then is how well chiral symmetry is realized for a finite and manageable value of N₅. We are studying this question in the high temperature (plasma) phase on a set of 16³ × 8 quenched configurations.

Computational Approach

The calculation of the eigenmodes of the domain-wall Dirac operator and the inversion of this operator to calculate the required greens functions is performed using the conjugate gradient method. The code is vectorized for PVP execution over the sites of the 4-dimensional lattice. We use the red-black preconditioning developed for Wilson fermions.

Accomplishments

We first determined the level crossings as a function of mass for Wilson fermions, which correspond to instantons in the gauge field configurations, for configurations with = 6/g² = 6.2, = 6.1 and = 6.0. We then calculated lowest lying eigenmodes of the domain-wall Dirac operator on each configuration as a function of N₅. For = 6.2, well above the transition, the eigenvalues separated into those which rapidly approached a non-zero limit as N₅ was increased, and those which appeared to be approaching zero exponentially with increasing N₅, and could be interpreted as the expected fermion zero modes corresponding to instantons. By = 6.0, which is very near the finite temperature phase transition, there was no clear separation.

At our highest value of N₅ (10), we calculated the connected and disconnected contributions to the n/n' and screening propagators at = 6.2 and are repeating this analysis at = 6.0. We are able to make an accurate calculation of the disconnected propagators by separating off the contribution of the lowest lying eigenmodes and using 20 noise vectors to get a stochastic estimator of the remainder. In the process of this calculation, we obtain estimates of the scalar and pseudoscalar chiral condensates for each configuration. The pseudoscalar condensate approximates the value predicted by the Atiyah-Singer theorem down to quark masses comparable with the value(s) of the would-be zero mode(s).

The screening propagators at = 6.2 approximate the correct chiral behavior. Those configurations identified with having topological charge zero make contributions consistent with zero to the disconnected propagators, while those with topological charge one make large contributions to the disconnected propagators, contributions which increase with decreasing quark mass (see figure). In the topological charge one sector, the "zero" mode contributions extracted from the connected propagator are in good agreement with the disconnected propagator. Indications are that the situation at = 6.0 is more complicated.

Configurations identified with topological charge one make large contributions to the disconnected propagators, contributions which increase with decreasing quark mass.

Significance

Publications

J.-F. Lagaë and D. K. Sinclair, "Domain wall fermions at finite temperature," Nucl. Phys. B (Proc. Suppl.) 73, 450 (1999).

J. B. Kogut, J.-F. Lagaë, and D. K. Sinclair, "Thermodynamics of lattice QCD with massless quarks and chiral four fermion interactions," Nucl. Phys. B (Proc. Suppl.) 73, 471 (1999).

J.-F. Lagaë and D. K. Sinclair, "Improved staggered quark actions with reduced flavour symmetry violations for lattice QCD," Phys. Rev. D 59, 014511 (1999).