Overlap Fermions on a $20^4$ Lattice

TL;DR

This paper presents results on hadron masses, quark masses, and chiral logs using overlap fermions on a large quenched lattice, demonstrating feasibility and topological effects in pion mass behavior.

Contribution

It provides the first large-scale quenched lattice calculation with overlap fermions, utilizing an improved gauge action to reduce eigenvalue density and enable feasible computations.

Findings

Pion mass approaches a constant for non-zero topological charge.

Pion mass tends to zero for trivial topology as quark mass decreases.

Improved gauge action reduces small eigenvalues, facilitating large lattice calculations.

Abstract

We report results on hadron masses, fitting of the quenched chiral log, and quark masses from Neuberger's overlap fermion on a quenched $20^4$ lattice with lattice spacing $a = 0.15$ fm. We used the improved gauge action which is shown to lower the density of small eigenvalues for $H^2$ as compared to the Wilson gauge action. This makes the calculation feasible on 64 nodes of CRAY-T3E. Also presented is the pion mass on a small volume ($6^3 \times 12$ with a Wilson gauge action at $\beta = 5.7$). We find that for configurations that the topological charge $Q \ne 0$, the pion mass tends to a constant and for configurations with trivial topology, it approaches zero possibly linearly with the quark mass.