Fermion-sign-free Majarana-quantum-Monte-Carlo studies of quantum critical phenomena of Dirac fermions in two dimensions

TL;DR

This paper employs a novel fermion-sign-free Majorana quantum Monte Carlo method to accurately study quantum critical phenomena of two-component Dirac fermions in 2+1 dimensions, revealing critical exponents that differ from mean-field predictions.

Contribution

The study introduces and applies a fermion-sign-free Majorana quantum Monte Carlo method to investigate quantum criticality of Dirac fermions, providing precise critical exponents for the Gross-Neveu chiral-Ising universality class.

Findings

Critical exponents differ from mean-field results.

Results align reasonably with renormalization group calculations.

Method enables accurate simulations of fermionic quantum critical phenomena.

Abstract

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 (MQMC) method introduced by us in Ref. [1], we investigate the quantum critical phenomena of {\it spinless} Dirac fermions at their charge-density-wave (CDW) 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 {\it two} (two-component) Dirac fermions in 2+1D: $\eta=0.45(2)$, $\nu=0.77(3)$, and $\beta=0.60(3)$, which are qualitatively different from the mean-field results but are reasonably close to the ones obtained from renormalization group calculations.