Fermion-sign-free Majarana-quantum-Monte-Carlo studies of quantum critical phenomena of Dirac fermions in two dimensions - Zi-Xiang Li; Yi-Fan Jiang; Hong Yao (New Journal of Physics, 2015)
Quantum critical phenomena may be qualitatively different when massless Dirac fermions are present at criticality. Using our recently-discovered fermion-sign-free Majorana quantum Monte Carlo method introduced by us in (Li et al 2015 Phys. Rev. B http://dx.doi.org/10.1103/physrevb.91.241117 91 http://dx.doi.org/10.1103/physrevb.91.241117 ), we investigate the quantum critical phenomena of spinless Dirac fermions at their charge-density-wave phase transitions on the honeycomb lattice having ${N}_{s}=2L^{2}$ sites with largest L = 24. By finite-size scaling, we accurately obtain critical exponents of this so-called Gross–Neveu chiral-Ising universality class of two (two-component) Dirac fermions in 2+1D: $η =0.45(2)$ , $ν =0.77(3)$ , and $β =0.60(3)$ , which are qualitatively different from the mean-field results but are reasonably close to the ones obtained from renormalization group calculations.