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

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.

10 pages, Proceedings of the 39th International Symposium on Lattice Field Theory, 8th-13th August 2022, Rheinische Friedrich-Wilhelms-Universität Bonn, Germany

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Cited by in corpus (5)

• Computing the Mass Shift of Wilson and Staggered Fermions in the Lattice Schwinger Model with Matrix Product States
• Simple Hamiltonian for Quantum Simulation of Strongly Coupled 2+1D SU(2) Lattice Gauge Theory on a Honeycomb Lattice
• Exploring the CP-violating Dashen phase in the Schwinger model with tensor networks
• Studying the phase diagram of the three-flavor Schwinger model in the presence of a chemical potential with measurement- and gate-based quantum computing
• Parton Distribution Functions in the Schwinger model from Tensor Network States