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arXiv · 1411.7383

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
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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.

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Zi-Xiang Li, Yi-Fan Jiang, Hong Yao. 2014-11-26. Fermion-sign-free Majarana-quantum-Monte-Carlo studies of quantum critical phenomena of Dirac fermions in two dimensions. https://doi.org/10.1088/1367-2630%2F17%2F8%2F085003

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