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arXiv:2501.14086 · International Symposium on Lattice Field Theory (LATTICE)

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

Hayato Kanno, Shinichiro Akiyama, Kotaro Murakami, Shinji Takeda

Published Jan 23, 2025• 0 citations
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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.

DOI
10.22323/1.466.0368

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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.
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