Spectral properties and chiral symmetry violations of (staggered) domain wall fermions in the Schwinger model

TL;DR

This paper investigates the spectral properties and chiral symmetry violations of various staggered domain wall fermion formulations in the Schwinger model, providing insights into their effectiveness and differences.

Contribution

It introduces and compares multiple staggered domain wall fermion formulations, including truncated and optimal variants, in the context of the Schwinger model.

Findings

Different formulations show varying degrees of chiral symmetry violation.

Spectral properties depend on the choice of kernels and construction methods.

Optimal formulations reduce chiral symmetry violations compared to standard ones.

Abstract

We follow up on a suggestion by Adams and construct explicit domain wall fermion operators with staggered kernels. We compare different domain wall formulations, namely the standard construction as well as Borici's modified and Chiu's optimal construction, utilizing both Wilson and staggered kernels. In the process, we generalize the staggered kernels to arbitrary even dimensions and introduce both truncated and optimal staggered domain wall fermions. Some numerical investigations are carried out in the (1+1)-dimensional setting of the Schwinger model, where we explore spectral properties of the bulk, effective and overlap Dirac operators in the free-field case, on quenched thermalized gauge configurations and on smooth topological configurations. We compare different formulations using the effective mass, deviations from normality and violations of the Ginsparg-Wilson relation as measures of chirality.