Chiral Heisenberg Gross-Neveu-Yukawa criticality: Honeycomb vs. SLAC fermions

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 semi-metal 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 super-exchange 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 $L\ge 15$ are considered. In contrast to the SLAC formulation, where the anomalous dimensions are estimated to be ${\eta }_{\varphi }=0.73(1)$ and ${\eta }_{\psi }=0.09(1)$, they remain less stable on honeycomb lattices, but tend towards the estimates from the SLAC formulation.

Comments: 17 pages, 18 figures