Chiral Heisenberg Gross-neveu-yukawa Criticality: Honeycomb Versus Slac Fermions

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 nu = 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 eta phi = 0.73(1) and eta psi = 0.09(1), they remain less stable on honeycomb lattices, but tend towards the estimates from the SLAC formulation.