2020/09/30 by Yuichi Otsuka, Kazuhiro Seki, Sandro Sorella +1 · 1 citation
Physics and Astronomy · #cond-mat.str-el
paper · pdf · doi:10.1103/physrevb.102.235105
published as Phys. Rev. B 102, 235105 (2020) · 12 pages, 12 figures
arxiv created 2020/12/02 · arxiv updated 2020/12/03
We numerically investigate the quantum criticality of the chiral Heisenberg universality class with the total number of fermion components N=8 in terms of the Gross-Neveu theory. Auxiliary-field quantum Monte Carlo simulations are performed for the square lattice Hubbard model in the presence of a d-wave pairing field, inducing Dirac cones in the single particle spectrum. This property makes the model particularly interesting because it turns out to belong to the same universality class of the Hubbard model on the honeycomb lattice, that is the canonical model for graphene, despite the unit cells being apparently different (e.g. they contain one and two sites, respectively). We indeed show that the two phase transitions, expected to occur on the square and on the honeycomb lattices, have the same quantum criticality. We also argue that details of the models, i.e., the way of counting N and the anisotropy of the Dirac cones, do not change the critical exponents. The present estimates of the exponents for the N=8 chiral Heisenberg universality class are ν=1.05(5), ηϕ=0.75(4), and ηψ=0.23(4), which are compared with the previous numerical estimations.