Mass Renormalization of the Schwinger Model with Wilson and Staggered Fermions in the Hamiltonian Lattice Formulation

TL;DR

This paper investigates the mass renormalization in the lattice Schwinger model using Wilson and staggered fermions within the Hamiltonian framework, introducing a new method to measure the mass shift and improve continuum extrapolations.

Contribution

It presents a novel Hamiltonian-based method to determine the mass shift for Wilson fermions and compares results with staggered fermions and analytical predictions.

Findings

Mass shift depends on lattice parameters and is crucial for accurate continuum extrapolation.

Incorporating the mass shift improves the agreement with analytical mass perturbation theory.

Comparison between Wilson and staggered fermions reveals differences in mass renormalization behavior.

Abstract

Lattice computations in the Hamiltonian formulation have so far mainly focused on staggered fermions. In these proceedings, we study Wilson fermions in the Hamiltonian formulation and propose a new method to determine the resulting mass shift. As a benchmark study, we examine the one-flavour Schwinger model with Wilson fermions and a topological $\theta$-term using matrix product states. Wilson fermions explicitly break chiral symmetry; thus, the bare mass of the lattice model receives an additive renormalization. In order to measure this mass shift directly, we develop a method that is suitable for the Hamiltonian formulation, which relies on the fact that the vacuum expectation value of the electric field density vanishes when the renormalized mass is zero. We examine the dependence of the mass shift on the lattice spacing, the lattice volume, the $\theta$-parameter, and the Wilson parameter. Using the mass shift, we then perform the continuum extrapolation of the electric field density and compare the resulting mass dependence to the analytical predictions of mass perturbation theory. We demonstrate that incorporating the mass shift significantly improves the continuum extrapolation. Finally, we apply our method to the same model using staggered fermions instead of Wilson fermions and compare the resulting mass shift to recent theoretical predictions.