Caution on Gross-Neveu criticality with a single Dirac cone: Violation of locality and its consequence of unexpected finite-temperature transition

Lately there are many SLAC fermion investigations on the (2 + 1)D Gross-Neveu criticality of a single Dirac cone. While the SLAC fermion construction indeed gives rise to the linear energy-momentum relation for all lattice momenta at the noninteracting limit, the long-range hopping and its consequent violation of locality on the Gross-Neveu quantum critical point (GN-QCP)-which a priori requires short-range interaction-has not been verified. Here we show, by means of large-scale quantum Monte Carlo simulations, that the interaction-driven antiferromagnetic insulator in this case is fundamentally different from that on a purely local pi-flux Hubbard model on the square lattice. In particular, the antiferromagnetic long-range order has a finite temperature continuous phase transition, which appears to violate the Mermin-Wagner theorem, and smoothly connects to the previously determined GN-QCP. The magnetic excitations inside the antiferromagnetic insulator are gapped without Goldstone mode, even though the state spontaneously breaks continuous SU (2) symmetry. These unusual results point out the fundamental difference between the QCP in SLAC fermion and that of GN-QCP with short-range interaction.

Automated summary

Recently, there have been many studies on the (2 + 1)D Gross-Neveu criticality of a single Dirac cone using SLAC fermion investigations. While SLAC fermion construction does show a linear energy-momentum relation for all lattice momenta at the noninteracting limit, the question of long-range hopping and its violation of locality on the Gross-Neveu quantum critical point (GN-QCP), which requires short-range interaction, has not been verified. In this study, large-scale quantum Monte Carlo simulations demonstrate that the interaction-driven antiferromagnetic insulator in this case is fundamentally different from that of a purely local pi-flux Hubbard model on the square lattice. Particularly, the antiferromagnetic long-range order undergoes a finite temperature continuous phase transition, seemingly violating the Mermin-Wagner theorem, and smoothly connects to the previously determined GN-QCP. The magnetic excitations inside the antiferromagnetic insulator are gapped without a Goldstone mode, even though the state spontaneously breaks continuous SU (2) symmetry. These unusual findings highlight the fundamental difference between the QCP in SLAC fermion and that of GN-QCP with short-range interaction.