Nature of the spin liquid state of the Hubbard model on honeycomb lattice

TL;DR

This paper investigates the spin liquid phase in the Hubbard model on a honeycomb lattice by studying an effective $J_1-J_2$ spin model, revealing a $Z_2$ spin liquid state and phase transitions using variational Monte Carlo methods.

Contribution

It provides the first detailed analysis of the $Z_2$ spin liquid phase in the honeycomb lattice Hubbard model through an effective spin model and variational Monte Carlo.

Findings

Identifies a $Z_2$ spin liquid phase at $J_2/J_1 oughly 0.08$

Finds a phase transition to a dimerized state at higher $J_2/J_1$

Maps the phase diagram of the effective spin model on the honeycomb lattice

Abstract

Recent numerical work (Nature 464, 847 (2010)) indicates the existence of a spin liquid phase (SL) that intervenes between the antiferromagnetic and semimetallic phases of the half filled Hubbard model on a honeycomb lattice. To better understand the nature of this exotic phase, we study the quantum $J_1-J_2$ spin model on the honeycomb lattice, which provides an effective description of the Mott insulating region of the Hubbard model. Employing the variational Monte Carlo approach, we analyze the phase diagram of the model, finding a phase transition between antiferromagnet and an unusual $Z_2$ SL state at $J_2/J_1\approx 0.08$, which we identify as the SL phase of the Hubbard model. At higher $J_2/J_1\gtrsim 0.3$ we find a transition to a dimerized state with spontaneously broken rotational symmetry.