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

TLDR

A spin liquid is a quantum state with a charge gap but no conventional order, and its existence in two dimensions remains controversial, with recent reports suggesting the Hubbard model on a honeycomb lattice hosts such a phase between a semi‑metal and an antiferromagnetic insulator. We performed numerically exact quantum Monte Carlo simulations on honeycomb lattices up to 2592 sites to test for a spin‑liquid region. The simulations reveal no evidence of a spin liquid; instead, a direct continuous transition occurs between the semi‑metal and antiferromagnetic insulator.

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.