Resonating Valence Bond States with Trimer Motifs

Abstract

The trimer resonating valence bond (tRVB) state consisting of an equal-weight superposition of trimer coverings on a square lattice is proposed. A model Hamiltonian of the Rokhsar-Kivelson type for which the tRVB becomes the exact ground state is written. The state is shown to have $9^g$ topological degeneracy on genus g surface and support $Z_3$ vortex excitations. Correlation functions show exponential behavior with a very short correlation length consistent with the gapped spectrum. The classical problem of the degeneracy of trimer configurations is investigated by the transfer matrix method.

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Cited by in corpus (11)

• Gapless Kitaev Spin Liquid to Classical String Gas through Tensor Networks
• Trimer states with ${\mathbb{Z}}_3$ topological order in Rydberg atom arrays
• Spin-one bilinear-biquadratic model on a star lattice
• A gapped SU(3) spin liquid with Z_3 topological order
• ${\mathbb{Z}}_3$ Topological Order in Face Centered Cubic Quantum Plaquette Model
• Proposal of a spin-one chain model with competing dimer and trimer interactions
• SU(3) trimer resonating-valence-bond state on the square lattice
• Quantum trimer models and topological SU(3) spin liquids on the kagome lattice
• Trimer classical spin liquid from interacting fractional charges
• Exact hole-induced $SU(N)$ flavor-singlets in certain $U=\infty$ $SU(N)$ Hubbard models
• $Z_3$ topological order in the quantum dimer-pentamer model