Resonating Valence Bond States with Trimer Motifs

TL;DR

This paper introduces a trimer resonating valence bond (tRVB) state on a square lattice, demonstrating its topological properties, exact solvability, and gapped spectrum with short-range correlations, advancing understanding of quantum spin liquids.

Contribution

It proposes the tRVB state, constructs a Hamiltonian with this state as the exact ground state, and analyzes its topological degeneracy and excitations.

Findings

tRVB state has $9^g$ topological degeneracy on genus g surfaces

Supports $Z_3$ vortex excitations

Correlation functions decay exponentially with a short correlation length

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.