Finite-size effects on a lattice calculation

TL;DR

This paper investigates how finite-size effects and boundary conditions on a non-periodic lattice influence the calculation of bosonic mass in the Schwinger model, revealing issues with continuum limit accuracy and fermion doubling.

Contribution

It demonstrates the impact of homogeneous boundary conditions on fermion doubling and chiral invariance, and identifies the matrix responsible for fermion doubling in lattice calculations.

Findings

Homogeneous boundary conditions eliminate fermion doubling and chiral invariance.

The lattice model does not produce the correct boson mass in the continuum limit.

The matrix causing fermion doubling is explicitly identified.

Abstract

We study in this paper the finite-size effects of a non-periodic lattice on a lattice calculation. To this end we use a finite lattice equipped with a central difference derivative with homogeneous boundary conditions to calculate the bosonic mass associated to the Schwinger model. We found that the homogeneous boundary conditions produce absence of fermion doubling and chiral invariance, but we also found that in the continuum limit this lattice model does not yield the correct value of the boson mass as other models do. We discuss the reasons for this and, as a result, the matrix which cause the fermion doubling problem is identified.