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 <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mrow> <a:mi>ν</a:mi> <a:mo>=</a:mo> <a:mn>1.02</a:mn> <a:mo>(</a:mo> <a:mn>3</a:mn> <a:mo>)</a:mo> </a:mrow> </a:math> coincides for the two lattice types once honeycomb lattices of linear dimension <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:mrow> <b:mi>L</b:mi> <b:mo>&gt;</b:mo> <b:mn>15</b:mn> </b:mrow> </b:math> are considered. In contrast to the SLAC formulation, where the anomalous dimensions are estimated to be <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:mrow> <c:msub> <c:mi>η</c:mi> <c:mi>ϕ</c:mi> </c:msub> <c:mo>=</c:mo> <c:mn>0.73</c:mn> <c:mrow> <c:mo>(</c:mo> <c:mn>1</c:mn> <c:mo>)</c:mo> </c:mrow> </c:mrow> </c:math> and <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"> <d:mrow> <d:msub> <d:mi>η</d:mi> <d:mi>ψ</d:mi> </d:msub> <d:mo>=</d:mo> <d:mn>0.09</d:mn> <d:mrow> <d:mo>(</d:mo> <d:mn>1</d:mn> <d:mo>)</d:mo> </d:mrow> </d:mrow> </d:math> , they remain less stable on honeycomb lattices, but tend towards the estimates from the SLAC formulation.