Tensor network formulation of the massless Schwinger model with staggered fermions

Abstract

We construct a tensor network representation of the partition function for the massless Schwinger model on a two-dimensional lattice using staggered fermions. The tensor network representation allows us to include a topological term. Using a particular implementation of the tensor renormalization group we calculate the average plaquette and topological charge density for the theory. For a range of values of the coupling constant for the topological term, $\mathrm{\ensuremath{\Theta}}$, and the gauge coupling, $\ensuremath{\beta}$, we compare with results from hybrid Monte Carlo simulations when possible and find good agreement. In order to further understand the role of fermions and topology in this model, we compare calculations of the same observables in a similar model, the Abelian Higgs model.