Fermionic quantum critical point of spinless fermions on a honeycomb lattice

Spinless fermions on a honeycomb lattice provide a minimal realization of lattice Dirac fermions. Repulsive interactions between nearest neighbors drive a quantum phase transition from a Dirac semimetal to a charge-density-wave state through a fermionic quantum critical point, where the coupling of the Ising order parameter to the Dirac fermions at low energy drastically affects the quantum critical behavior. Encouraged by a recent discovery (Huffman and Chandrasekharan 2014 Phys. Rev. B http://dx.doi.org/10.1103/PhysRevB.89.111101 89 http://dx.doi.org/10.1103/PhysRevB.89.111101 ) of the absence of the fermion sign problem in this model, we study the fermionic quantum critical point using the continuous-time quantum Monte Carlo method with a worm-sampling technique. We estimate the transition point $V/t=1.356(1)$ with the critical exponents $\nu =0.80(3)$ and $\eta =0.302(7)$ . Compatible results for the transition point are also obtained with infinite projected entangled-pair states.