Phase diagram of the single-flavor Gross--Neveu--Wilson model from the Grassmann corner transfer matrix renormalization group

TL;DR

This paper maps the phase diagram of the single-flavor Gross--Neveu model with Wilson fermions using Grassmann tensor networks and CTMRG, identifying critical lines and phases, including topological insulators and the Aoki phase.

Contribution

It introduces a Grassmann CTMRG approach to analyze the phase structure of the model, revealing the nature of phase boundaries and the absence of the Aoki phase at strong coupling.

Findings

Aoki phase is separated by critical lines with central charge c=1/2.

Topological and trivial phases are separated by critical lines with c=1.

Aoki phase does not survive in the strong-coupling regime.

Abstract

We investigate the phase structure of the single-flavor Gross--Neveu model with Wilson fermions using the Grassmann corner transfer matrix renormalization group (CTMRG). The path integral is formulated as a two-dimensional Grassmann tensor network and approximately contracted by the Grassmann CTMRG algorithm. We investigate the phase diagram by varying the fermion mass and the four-fermion coupling, using the pseudoscalar condensate as an order parameter for the $\mathbb{Z}_{2}$ parity symmetry breaking phase. The universality classes of the phase boundaries are identified through the central charge $c$ obtained via scaling analysis of the entanglement entropy. Furthermore, we extract the quantity related to the entanglement spectrum from the converged CTMRG environments, allowing us to distinguish the topological insulator phase and the trivial phase. The resulting phase structure suggests that the Aoki phase is separated from the other phases by critical lines characterized by $c=1/2$, while the critical lines with $c=1$ separate the topological insulating and trivial phases. Our numerical results also indicate that the Aoki phase does not persist in the strong-coupling regime for the single-flavor theory.