Plaquette valence-bond ordering in J_1-J_2 Heisenberg antiferromagnet on the honeycomb lattice

TL;DR

This study investigates the ground state of the J_1-J_2 Heisenberg model on the honeycomb lattice, providing evidence for plaquette valence bond order in a specific frustration range and identifying a transition to a dimerized state.

Contribution

It demonstrates the effectiveness of the NNVB basis in describing the ground state and identifies a plaquette valence bond ordered phase in the frustrated regime.

Findings

Plaquette valence bond order exists for 0.2<J_2/J_1<0.3.

Transition from plaquette order to staggered dimerized state occurs at higher J_2/J_1.

NNVB basis accurately describes the ground state in the relevant parameter range.

Abstract

We study S=1/2 Heisenberg model on the honeycomb lattice with first and second neighbor antiferromagnetic exchange (J_{1}-J_{2} model), employing exact diagonalization in both S_z=0 basis and nearest neighbor singlet valence bond (NNVB) basis. We find that for 0.2<J_2/J_1<0.3, NNVB basis gives a proper description of the ground state in comparison with the exact results. By analyzing the dimer-dimer as well as plaquette-plaquette correlations and also defining appropriate structure factors, we investigate possible symmetry breaking states as the candidate for the ground state in the frustrated region. We provide body of evidences in favor of plaquette valence bond ordering for 0.2<J_2/J_1<0.3. By further increasing the ratio J_2/J_1, this state undergoes a transition to the staggered dimerized state.