Chiral Ising Gross-Neveu Criticality of a Single Dirac Cone: A Quantum Monte Carlo Study

Abstract

We perform large-scale quantum Monte Carlo simulations of SLAC fermions on a two-dimensional square lattice at half filling with a single Dirac cone with N=2 spinor components and repulsive on-site interactions. Despite the presence of a sign problem, we accurately identify the critical interaction strength U_{c}=7.28±0.02 in units of the hopping amplitude, for a continuous quantum phase transition between a paramagnetic Dirac semimetal and a ferromagnetic insulator. Using finite-size scaling, we extract the critical exponents for the corresponding N=2 chiral Ising Gross-Neveu universality class: the inverse correlation length exponent ν^{-1}=1.19±0.03, the order parameter anomalous dimension η_{ϕ}=0.31±0.01, and the fermion anomalous dimension η_{ψ}=0.136±0.005.