Fermionic quantum criticality in honeycomb and $\pi$-flux Hubbard models: Finite-size scaling of renormalization-group-invariant observables from quantum Monte Carlo

TL;DR

This study uses quantum Monte Carlo simulations to analyze the critical behavior of the Hubbard model on honeycomb and $$-flux lattices, confirming it belongs to the Gross-Neveu-Heisenberg universality class.

Contribution

It introduces a finite-size scaling method with improved renormalization-group-invariant observables for accurate critical point estimation.

Findings

Critical couplings and exponents estimated accurately.

Transition belongs to the Gross-Neveu-Heisenberg universality class.

Method verified on the Kane-Mele-Hubbard model.

Abstract

We numerically investigate the critical behavior of the Hubbard model on the honeycomb and the $\pi$-flux lattice, which exhibits a direct transition from a Dirac semimetal to an antiferromagnetically ordered Mott insulator. We use projective auxiliary-field quantum Monte Carlo simulations and a careful finite-size scaling analysis that exploits approximately improved renormalization-group-invariant observables. This approach, which is successfully verified for the three-dimensional XY transition of the Kane-Mele-Hubbard model, allows us to extract estimates for the critical couplings and the critical exponents. The results confirm that the critical behavior for the semimetal to Mott insulator transition in the Hubbard model belongs to the Gross-Neveu-Heisenberg universality class on both lattices.