Abstract
We have made a detailed study of the phase structure for lattice Schwinger model with one flavor of Wilson fermion on the $(m,g)$ plane. For numerical investigation, we develop a decorated tensor renormalization method for lattice gauge theories with fermions incorporating the Grassmann tensor renormalization. Our algorithm manifestly preserves rotation and reflection symmetries. We find not only a parity-broken phase but also a Berezinskii-Kosterlitz-Thouless (BKT) transition by evaluating the central charge and an expectation value of a projection operator into the parity-odd subspace. The BKT phase boundaries converge into the degenerated doubler pole $(m,g)=(-2,0)$, while the parity-breaking transition line ends at the physical pole $(m,g)=(0,0)$. In addition, our analysis of scaling dimensions indicates that a conformal field theory with $\mathrm{SU}(2)$ symmetry arises on the line of $m=-2$.
Highlights
The Wilson fermion is one of the standard lattice regularizations for the continuum Dirac fermion, avoiding the species-doubling problem
Schwinger model with one flavor of the Wilson fermion throughout the ðm; gÞ plane, we have improved our method proposed in Ref. [6], which was based on the tensor renormalization group (TRG) [8]
We have performed a detailed study of the phase structure of the lattice Schwinger model with one flavor of the Wilson fermion by developing a decorated Grassmann TRG method
Summary
The Wilson fermion is one of the standard lattice regularizations for the continuum Dirac fermion, avoiding the species-doubling problem. In this paper we develop a more efficient method to study the lattice Schwinger model with one flavor of the Wilson fermion by combining the ideas of the decorated TRG and Grassmann TRG, and investigate the phase structure in the region around m 1⁄4 −2 at finite couplings, which was out of reach in previous studies. It is worth noting that other tensor network methods are gathering much attention from the field of high energy physics They choose the analysis of the lattice Schwinger model as a pilot study, though the KogutSusskind fermion formulation has been employed so far in all such works [23,24,25,26,27,28,29,30,31,32,33,34,35,36].
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