The two flavour Schwinger model: scaling of the scalar condensate

TL;DR

This paper studies how the scalar condensate in the two-flavor Schwinger model behaves as the lattice spacing approaches zero, comparing different fermion discretizations and methods.

Contribution

It provides a detailed comparison of scalar condensate calculations using twisted mass and overlap fermions, revealing discrepancies and their resolution.

Findings

Large discrepancies between twisted mass and overlap fermions for the scalar condensate.

Discrepancies are resolved when using the point split current for twisted mass fermions.

Consistent results are obtained when using the same fermion discretization and method.

Abstract

We investigate the continuum limit scaling of the scalar condensate in the $N_f=2$ Schwinger model on the lattice. We employ maximally twisted mass Wilson fermions and overlap fermions. We compute the scalar condensate by taking the trace of the propagator (direct method) and by utilizing the integrated Ward-Takahashi identity. While the scalar condensate comes out consistent using these two methods for a given kind of lattice fermions, we find --quite surprisingly-- large discrepancies for the scalar condensate between twisted mass and overlap fermions. These discrepancies are only resolved when using the point split current for twisted mass fermions.