QMC study of the chiral Heisenberg Gross-Neveu universality class

TL;DR

This study uses large-scale quantum Monte Carlo simulations to demonstrate that the antiferromagnetic phase transition in a Hubbard model with a d-wave pairing field belongs to the chiral Heisenberg Gross-Neveu universality class, consistent across different lattice structures.

Contribution

It provides numerical evidence that the quantum criticality of the Hubbard model with a d-wave pairing field aligns with the chiral Heisenberg universality class, regardless of lattice details.

Findings

Both square and honeycomb lattice models exhibit the same quantum criticality.

Model details like fermion component count and Dirac cone anisotropy do not affect critical exponents.

Abstract

We investigate a quantum criticality of an antiferromagnetic phase transition in the Hubbard model on a square lattice with a $d$-wave pairing field by large-scale auxiliary-field quantum Monte Carlo simulations. Since the $d$-wave pairing filed induces Dirac cones in the non-interacting single-particle spectrum, the quantum criticality should correspond to the chiral Heisenberg universality class in terms of the Gross-Neveu theory, which is the same as those expected in the Hubbard model on the honeycomb lattice, despite the unit cells being different (e.g., they contain one and two sites, respectively). We show that both the two phase transitions, expected to occur on the square and on the honeycomb lattices, indeed have the same quantum criticality. We also argue that details of the models, i.e., the way of counting the total number $N$ of fermion components and the anisotropy of the Dirac cones, do not change the critical exponents.