Plaquette-RVB state in the Frustrated Honeycomb Antiferromagnet

Abstract

We study the proposed plaquette-RVB (pRVB) state in the honeycomb lattice $J_1-J_2$ 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 $J_2/J_1$. The pRVB state is most stable around $J_2/J_1\sim 0.25$. We identify the wavevectors of the lowest triplet excitations, which can be verified using exact diagonalization or DMRG studies. When $J_2$ is reduced, we can have either a deconfined Quantum Phase Transition (QPT) or a first-order transition into a Néel state. When $J_2$ is increased, we surmise that the system undergoes a first order phase transition into a state which breaks lattice rotational symmetry.

9 pages, 9 figures, minor corrections

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• Emergence of string-valence bond solid state in the frustrated $J_1-J_2$ transverse field Ising model on the square lattice
• Deconfined Quantum Critical Point: A Review of Progress
• Holes Localized on a Skyrmion in a Doped Antiferromagnet on the Honeycomb Lattice: Symmetry Analysis
• Frustrated spin-$\frac{1}{2}$ Heisenberg magnet on an $AA$-stacked honeycomb bilayer: High-order study of the collinear magnetic phases of the $J_1$--$J_2$--$J_1^{\perp }$ model
• Valence Bond Phases in $S=1/2$ Kane-Mele-Heisenberg Model
• Nesting instability of gapless U(1) spin liquids with spinon Fermi pockets in two dimensions