Weak plaquette valence bond order in the $S=1/2$ honeycomb $J_1-J_2$ Heisenberg model

TL;DR

This study uses DMRG to explore the phase diagram of the $S=1/2$ honeycomb $J_1-J_2$ Heisenberg model, revealing a paramagnetic phase with potential weak plaquette valence bond order near $J_2/J_1 \,\sim\, 0.3$.

Contribution

First detailed DMRG investigation of the honeycomb $J_1-J_2$ model revealing possible weak PVB order and criticality in the intermediate phase.

Findings

Identification of a paramagnetic phase near $J_2/J_1 \sim 0.3$

Observation of growing correlation length indicating criticality or weak order

Boundaries between antiferromagnetic, paramagnetic, and valence bond crystal phases

Abstract

Using the density matrix renormalization group, we investigate the $S=1/2$ Heisenberg model on the honeycomb lattice with first- ($J_1$) and second-neighbor ($J_2$) interactions. We are able to study long open cylinders with widths up to 12 lattice spacings. For $J_2/J_1$ near 0.3, we find an apparently paramagnetic phase, bordered by an antiferromagnetic phase for $J_2\lesssim 0.26$ and by a valence bond crystal for $J_2\gtrsim 0.36$. The longest correlation length that we find in this intermediate phase is for plaquette valence bond (PVB) order. This correlation length grows strongly with cylinder circumference, indicating either quantum criticality or weak PVB order.