Abstract
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 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 with the critical exponents and . Compatible results for the transition point are also obtained with infinite projected entangled-pair states.
Highlights
Interaction-induced quantum phase transitions of Dirac fermions are of general interest in graphene [2], d-wave superconductors [3], topological insulators [4], ultracold atoms [5] and high-energy physics [6]
We presented a sign-problem-free continuous-time quantum Monte Carlo (CTQMC) study of the Dirac semi-metal to charge-densitywave transition on a honeycomb lattice and compare it with theory and infinite-projected entangled-pair states (iPEPS) results
Our main results about the transition point and the critical exponents are summarized in table 1
Summary
Interaction-induced quantum phase transitions of Dirac fermions are of general interest in graphene [2], d-wave superconductors [3], topological insulators [4], ultracold atoms [5] and high-energy physics [6]. One of the prototypical examples consists of half-filled spinless. Fermions on a honeycomb lattice interacting through nearest-neighbor repulsions H = H0 + H1, (1). ( ) H0 = −t∑ ci†cj + cj†ci = ∑ci†Kijcj, (2) i,j i,j H1 = V ∑
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