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arXiv · 2210.04272

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

Yuan Da Liao·Xiao Yan Xu·Zi Yang Meng·Yang Qi
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Abstract

Lately there are many SLAC fermion investigations on the (2+1)D Gross-Neveu criticality of a single Dirac cone [1,2]. While the SLAC fermion construction indeed gives rise to the linear energy-momentum relation for all lattice momenta at the non-interacting 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, we find the antiferromagnetic long-range order in the SLAC fermion model has a finite temperature continuous phase transition, which violates 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 proclaim caution on the interpretation of the quantum phase transition in SLAC fermion model as that of GN-QCP with short-range interaction.

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Yuan Da Liao, Xiao Yan Xu, Zi Yang Meng, Yang Qi. 2022-10-09. Caution on Gross-Neveu criticality with a single Dirac cone: Violation of locality and its consequence of unexpected finite-temperature transition. https://doi.org/10.1103/physrevb.108.195112

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