Fermionic Quantum Critical Point of Spinless Fermions on a Honeycomb Lattice

TL;DR

This paper investigates the quantum critical point in a honeycomb lattice of spinless fermions, revealing how interactions induce a phase transition and analyzing critical behavior using advanced computational methods.

Contribution

It provides the first detailed study of the fermionic quantum critical point in this model, combining quantum Monte Carlo and tensor network techniques to estimate critical parameters.

Findings

Transition point at V/t=1.356(1)

Critical exponents: ν=0.80(3), η=0.302(7)

Consistent results from different computational methods

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 Ising order parameter to the Dirac fermions at low energy drastically affects the quantum critical behavior. Encouraged by a recently discovery of 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 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.