Violation of chirality of the M\"obius domain-wall Dirac operator from the eigenmodes

TL;DR

This paper examines how violations of the Ginsparg-Wilson relation in M"obius domain-wall fermions affect physical observables, especially low-lying eigenmodes, impacting chiral symmetry restoration at finite temperature.

Contribution

It provides a detailed eigenmode decomposition to isolate GW-violating effects in M"obius domain-wall fermions and analyzes their impact on physical quantities.

Findings

GW-violating effects are significant for low-lying eigenmodes.

Residual mass and meson susceptibilities are affected by GW violation.

Low-lying eigenmodes dominate the GW-violating contributions.

Abstract

We investigate the effects of the violation of the Ginsparg-Wilson (GW) relation in the M\"obius domain-wall fermion formulation on the lattice with finite fifth dimension. Using a decomposion in terms of the eigenmodes of its four-dimensional effective Dirac operator, we isolate the GW-violating terms for various physical quantities including the residual mass and the meson susceptibilities relevant for the effective restoration of the axial U(1) symmetry at finite temperature. Numerical result shows that the GW-violating effect is more significant, or even overwhelming, for the quantities that are dominated by the low-lying eigenmodes.