Antiferromagnetism in the Hubbard model on the honeycomb lattice: a Two-Particle Self-Consistent study

TL;DR

This study extends the two-particle self-consistent approach to the honeycomb lattice to analyze the antiferromagnetic transition in the Hubbard model, finding results consistent with quantum Monte Carlo simulations and exploring temperature-dependent magnetic properties.

Contribution

The paper introduces a generalized TPSC method for the honeycomb lattice and accurately estimates the critical interaction strength for antiferromagnetism.

Findings

Critical interaction strength Uc/t=3.79±0.01 for antiferromagnetic transition

Results align closely with quantum Monte Carlo data

Temperature-dependent correlation lengths and crossover temperatures analyzed

Abstract

The semimetal to antiferromagnet quantum phase transition of the Hubbard model on the honeycomb lattice has come to the forefront in the context of the proposal that a semimetal to spin liquid transition can occur before the transition to the antiferromagnetic phase. To study the semimetal to antiferromagnet transition, we generalize the two-particle self-consistent (TPSC) approach to the honeycomb lattice (a structure that can be realized in graphene for example). We show that the critical interaction strength where the transition occurs is $U_c/t=3.79\pm 0.01$ quite close to the value $U_c/t=3.869 \pm 0.013$ reported using large-scale quantum Monte Carlo simulations. This reinforces the conclusion that the semimetal to spin liquid transition is pre-empted by the transition to the antiferromagnet. Since TPSC satisfies the Mermin-Wagner theorem, we find temperature-dependent results for the antiferromagnetic and ferromagnetic correlation lengths as well as the dependence of double occupancy and of the renormalized spin and charge interactions on the bare interaction strength. We also estimate the value of the crossover temperature to the renormalized classical regime as a function of interaction strength.