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

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 nu(-1) = 1.19 +/- 0.03, the order parameter anomalous dimension eta(phi) = 0.31 +/- 0.01, and the fermion anomalous dimension eta(psi) = 0.136 +/- 0.005.

Automated summary

In this study, we performed large-scale quantum Monte Carlo simulations to investigate the behavior of SLAC fermions on a two-dimensional square lattice. We accurately identified the critical interaction strength and extracted the corresponding critical exponents.