Chiral Ising Gross-Neveu criticality of a single Dirac cone: A quantum Monte Carlo study

TL;DR

This study uses quantum Monte Carlo simulations to precisely determine the critical interaction strength and critical exponents of a quantum phase transition in a single Dirac cone system, revealing its chiral Ising Gross-Neveu universality class.

Contribution

First large-scale QMC study of a single Dirac cone with N=2, accurately identifying critical parameters despite the sign problem.

Findings

Critical interaction strength U_c = 7.28 ± 0.02

Critical exponents: ν^{-1} = 1.19 ± 0.03, η_φ = 0.31 ± 0.01, η_ψ = 0.136 ± 0.005

Transition between Dirac semimetal and ferromagnetic insulator

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 $U_c = 7.28 \pm 0.02$ 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 $\nu^{-1} = 1.19 \pm 0.03$, the order parameter anomalous dimension $\eta_{\phi} = 0.31 \pm 0.01$, and the fermion anomalous dimension $\eta_{\psi} = 0.136 \pm 0.005$.