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We revisit the lattice formulation of the Schwinger model using theKogut-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 toprovide the lattice regularization of the massless Schwinger model. We insteadargue that the relation between the lattice and continuum mass parametersshould be taken as $m_{\rm lat}=m- \frac 18 e^2 a$. The model with $m=0$ isshown to possess a discrete chiral symmetry that is generated by the unitlattice translation accompanied by the shift of the $\theta$-angle by $\pi$.While the mass shift vanishes as the lattice spacing $a$ approaches zero, wefind that including this shift greatly improves the rate of convergence to thecontinuum limit. We demonstrate the faster convergence using both numericaldiagonalizations of finite lattice systems, as well as extrapolations of thelattice strong coupling expansions.

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