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 𝜃-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 𝜃-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.

Review on Quantum Computing for Lattice Field Theory

“…[4,5] for reviews and Refs. [55][56][57][58][59][60][61][62][63][64][65] for more recent studies not included in Refs. [4,5].…”

“…Recently, there has been progress with the implementation of Wilson fermions in the Hamiltonian formulation (see, e.g., Refs. [136,137]) and with determining the resulting mass shift [61].…”

T-mu phase diagram using classical-quantum hybrid algorithm

“…The Lefschetz thimble algorithm is a similar approach, but it is an exact algorithm [17][18][19][20]. These methods are classified as classical algorithms, but there are also tensor network-based methods [21][22][23][24][25][26][27].…”

Computing the Mass Shift of Wilson and Staggered Fermions in the Lattice Schwinger Model with Matrix Product States

“…In this paper, we extend the work done in Ref. [29] and present a method to compute the mass shift in the Hamiltonian formulation, focusing on the Schwinger model with a topological θ-term as a benchmark model. The knowledge of the mass shift allows for following lines of constant renormalized mass.…”