QMC study of the chiral Heisenberg Gross-Neveu universality class

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.

5 pages, 3 figures, proceeding for the XXXII IUPAP Conference on Computational Physics (CCP2021)

References in corpus (6)

• Quantum spin-liquid emerging in two-dimensional correlated Dirac fermions
• Absence of a Spin Liquid Phase in the Hubbard Model on the Honeycomb Lattice
• Fermionic quantum criticality in honeycomb and $\pi$-flux Hubbard models: Finite-size scaling of renormalization-group-invariant observables from quantum Monte Carlo
• Comprehensive quantum Monte Carlo study of the quantum critical points in planar dimerized/quadrumerized Heisenberg models
• The Antiferromagnetic Character of the Quantum Phase Transition in the Hubbard Model on the Honeycomb Lattice
• Mott physics in the half-filled Hubbard model on a family of vortex-full square lattices

Cited by in corpus (2)

• Chiral Heisenberg Gross-Neveu-Yukawa criticality: Honeycomb vs. SLAC fermions
• Phase diagram and critical behavior of Hubbard model on the square-hexagon-octagon lattice