Discrete Chiral Symmetry and Mass Shift in Lattice Hamiltonian Approach to Schwinger Model

TL;DR

This paper revisits the lattice formulation of the Schwinger model, revealing a mass shift that enhances continuum limit convergence and highlighting a discrete chiral symmetry at zero mass.

Contribution

It introduces a corrected relation between lattice and continuum mass parameters, improving the convergence to the continuum limit in lattice simulations of the Schwinger model.

Findings

Mass shift improves convergence to continuum limit

Discrete chiral symmetry exists at zero lattice mass

Numerical and analytical methods confirm faster convergence

Abstract

We revisit the lattice formulation of the Schwinger model using the Kogut-Susskind Hamiltonian approach with staggered fermions. This model, introduced by Banks et al., contains the mass term $m_{\rm lat} \sum_{n} (-1)^{n} \chi^\dagger_n \chi_n$, and setting it to zero is often assumed to provide the lattice regularization of the massless Schwinger model. We instead argue that the relation between the lattice and continuum mass parameters should be taken as $m_{\rm lat}=m- \frac 18 e^2 a$. The model with $m=0$ is shown to possess a discrete chiral symmetry that is generated by the unit lattice translation accompanied by the shift of the $\theta$-angle by $\pi$. While the mass shift vanishes as the lattice spacing $a$ approaches zero, we find that including this shift greatly improves the rate of convergence to the continuum limit. We demonstrate the faster convergence using both numerical diagonalizations of finite lattice systems, as well as extrapolations of the lattice strong coupling expansions.