Absence of a Spin Liquid Phase in the Hubbard Model on the Honeycomb Lattice

TL;DR

This study uses large-scale quantum Monte Carlo simulations to investigate the Hubbard model on the honeycomb lattice, finding no strong evidence for a spin liquid phase and instead indicating a direct transition between semi-metal and antiferromagnetic insulator phases.

Contribution

The paper provides the first large-cluster numerical evidence challenging the existence of a spin liquid phase in the Hubbard model on the honeycomb lattice.

Findings

No strong evidence of a spin liquid phase.

Indicates a direct, continuous transition between phases.

Larger cluster simulations improve previous results.

Abstract

A spin liquid is a novel quantum state of matter with no conventional order parameter where a finite charge gap exists even though the band theory would predict metallic behavior. Finding a stable spin liquid in two or higher spatial dimensions is one of the most challenging and debated issues in condensed matter physics. Very recently, it has been reported that a model of graphene, i.e., the Hubbard model on the honeycomb lattice, can show a spin liquid ground state in a wide region of the phase diagram, between a semi-metal (SM) and an antiferromagnetic insulator (AFMI). Here, by performing numerically exact quantum Monte Carlo simulations, we extend the previous study to much larger clusters (containing up to 2592 sites), and find, if any, a very weak evidence of this spin liquid region. Instead, our calculations strongly indicate a direct and continuous quantum phase transition between SM and AFMI.