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

TL;DR

This paper investigates the phase structure of the lattice Schwinger model with one flavor of Wilson fermion, revealing a BKT transition and parity-breaking phases using a novel tensor renormalization method.

Contribution

The study introduces a decorated tensor renormalization algorithm for lattice gauge theories with fermions that preserves symmetries and identifies BKT and parity-breaking phases.

Findings

Identification of a BKT transition in the model.

Convergence of phase boundaries at the degenerated doubler pole.

Emergence of an SU(2) symmetric conformal field theory at a specific line.

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 $m=-2$.