Lattice gauge action suppressing near-zero modes of H_W

TL;DR

This paper introduces a lattice action with unphysical Wilson fermions to suppress near-zero modes of H_W, facilitating more efficient dynamical overlap fermion simulations by creating a spectral gap and reducing computational costs.

Contribution

The authors propose a new lattice action that suppresses near-zero modes of H_W, enabling feasible dynamical overlap fermion simulations with reduced computational effort.

Findings

Spectral gap near lambda_W=0 observed with the new action.

Numerical cost for matrix sign function calculation is significantly reduced.

Topological charge remains conserved during gauge field evolution.

Abstract

We propose a lattice action including unphysical Wilson fermions with a negative mass m_0 of the order of the inverse lattice spacing. With this action, the exact zero mode of the hermitian Wilson-Dirac operator H_W(m_0) cannot appear and near-zero modes are strongly suppressed. By measuring the spectral density rho(lambda_W), we find a gap near lambda_W=0 on the configurations generated with the standard and improved gauge actions. This gap provides a necessary condition for the proof of the exponential locality of the overlap-Dirac operator by Hernandez, Jansen, and Luescher. Since the number of near-zero modes is small, the numerical cost to calculate the matrix sign function of H_W(m_0) is significantly reduced, and the simulation including dynamical overlap fermions becomes feasible. We also introduce a pair of twisted mass pseudo-fermions to cancel the unwanted higher mode effects of the Wilson fermions. The gauge coupling renormalization due to the additional fields is then minimized. The topological charge measured through the index of the overlap-Dirac operator is conserved during continuous evolutions of gauge field variables.