Plaquette-RVB state in the Frustrated Honeycomb Antiferromagnet

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We study the proposed plaquette-RVB (pRVB) state in the honeycomb lattice J₁-J₂ model with frustration arising from next-nearest neighbour interactions. Starting with the limit of decoupled hexagons, we develop a plaquette operator approach to describe the pRVB state and its low energy excitations. Our calculation clarifies that the putative pRVB state necessarily has f-wave symmetry - the plaquette wavefunction is an antisymmetric combination of the Kekulé structures. We estimate the plaquette ordering amplitude, ground state energy and spin gap as a function of J₂/J₁. The pRVB state is most stable around J₂/J₁ 0.25. We identify the wavevectors of the lowest triplet excitations, which can be verified using exact diagonalization or DMRG studies. When J₂ is reduced, we can have either a deconfined Quantum Phase Transition (QPT) or a first-order transition into a Néel state. When J₂ is increased, we surmise that the system undergoes a first order phase transition into a state which breaks lattice rotational symmetry.