Grassmann Tensor Renormalization Group for two-flavor massive Schwinger model with a theta term

TL;DR

This paper applies the Grassmann tensor renormalization group to study the two-flavor massive Schwinger model with a theta term, revealing phase structure differences from continuum predictions.

Contribution

It introduces a tensor network approach to analyze the massive two-flavor Schwinger model with a theta term, enabling non-perturbative lattice calculations.

Findings

Results agree with analytical solutions at large mass

Indicates different phase structure on lattice versus continuum

Demonstrates effectiveness of Grassmann tensor network methods

Abstract

We investigate the $N_f=2$ Schwinger model with the massive staggered fermions in the presence of a $2\pi$ periodic $\theta$ term, using the Grassmann tensor renormalization group. Thanks to the Grassmann tensor network formulation, there is no difficulty in dealing with the massive staggered fermions. We study the $\theta$ dependence of the free energy in the thermodynamic limit. Our calculation provides consistent results with the analytical solution in the large mass limit. The results also suggest that the $N_f=2$ Schwinger model on a lattice has a different phase structure from that described by the continuum theory.