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Chiral Heisenberg Gross-Neveu-Yukawa criticality: Honeycomb versus SLAC fermions

Thomas C. Lang1,* and Andreas M. Läuchli2,3

  • *Contact author: thomas.lang@uibk.ac.at
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Phys. Rev. B 112, 245121 – Published 8 December, 2025

DOI: https://doi.org/10.1103/vlgd-7ln8

Abstract

We perform large-scale quantum Monte Carlo simulations of the Hubbard model at half filling with a single Dirac cone close to the critical point, which separates a Dirac semimetal from an antiferromagnetically ordered phase where SU(2) spin rotational symmetry is spontaneously broken. We discuss the implementation of a single Dirac cone in the SLAC formulation for eight Dirac components and the influence of dynamically induced long-range superexchange interactions. The finite-size behavior of dimensionless ratios and the finite-size scaling properties of the Hubbard model with a single Dirac cone are shown to be superior compared to the honeycomb lattice. We extract the critical exponent believed to belong to the chiral Heisenberg Gross-Neveu-Yukawa universality class: the critical exponent ν=1.02(3) coincides for the two lattice types once honeycomb lattices of linear dimension L>15 are considered. In contrast to the SLAC formulation, where the anomalous dimensions are estimated to be ηϕ=0.73(1) and ηψ=0.09(1), they remain less stable on honeycomb lattices, but tend towards the estimates from the SLAC formulation.

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Phys. Rev. B 112, 245121– Published 8 December, 2025
  • Received 16 May 2025
  • Revised 12 September 2025
  • Accepted 24 October 2025
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