Berezinskii-Kosterlitz-Thouless transition in lattice Schwinger model with one flavor of Wilson fermion

We have made a detailed study of the phase structure for the 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 SU(2) symmetry arises on the line of m=-2.