Discrete chiral symmetry and mass shift in the lattice Hamiltonian approach to the Schwinger model

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. Phys. Rev. D 13, 1043 (1976), contains the mass term ${m}_{\mathrm{lat}}{\ensuremath{\sum}}_{n}{(\ensuremath{-}1)}^{n}{\ensuremath{\chi}}_{n}^{\ifmmode\dagger\else\textdagger\fi{}}{\ensuremath{\chi}}_{n}$, 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 ${m}_{\mathrm{lat}}=m\ensuremath{-}\frac{1}{8}{e}^{2}a$. 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 $\ensuremath{\theta}$ angle by $\ensuremath{\pi}$. 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.