Pinning the order: the nature of quantum criticality in the Hubbard model on honeycomb lattice

TL;DR

This study uses a pinning method in quantum Monte Carlo simulations to precisely characterize the quantum phase transition in the Hubbard model on a honeycomb lattice, revealing a continuous transition consistent with the Gross-Neveu universality class.

Contribution

The paper introduces an enhanced pinning technique to accurately determine the nature of quantum criticality in the Hubbard model on honeycomb lattices.

Findings

Identifies a continuous quantum phase transition between semi-metallic and antiferromagnetic states.

Finds the single particle gap correlates with staggered magnetization.

Critical exponents match the Gross-Neveu universality class.

Abstract

In numerical simulations, spontaneously broken symmetry is often detected by computing two-point correlation functions of the appropriate local order parameter. This approach, however, computes the square of the local order parameter, and so when it is {\it small}, very large system sizes at high precisions are required to obtain reliable results. Alternatively, one can pin the order by introducing a local symmetry breaking field, and then measure the induced local order parameter infinitely far from the pinning center. The method is tested here at length for the Hubbard model on honeycomb lattice, within the realm of the projective auxiliary field quantum Monte Carlo algorithm. With our enhanced resolution we find a direct and continuous quantum phase transition between the semi-metallic and the insulating antiferromagnetic states with increase of the interaction. The single particle gap in units of the Hubbard $U$ tracks the staggered magnetization. An excellent data collapse is obtained by finite size scaling, with the values of the critical exponents in accord with the Gross-Neveu universality class of the transition.