Spin Triplet Excitations for a Valence Bond Solid on the Kagome Lattice

TL;DR

This paper develops a theoretical model for triplet excitations in a valence bond solid on the Kagome lattice, revealing non-dispersive modes and quantum fluctuation effects, with implications for neutron scattering experiments.

Contribution

It provides a detailed bond operator theory of triplet spectra in the Kagome VBS, including quantum fluctuation effects and comparison with spin liquid phases.

Findings

Many triplet modes are non-dispersive.

The lowest triplet excitation is non-dispersive and degenerate at the zone center.

Quantum fluctuations lower the triplet gap.

Abstract

One of the most promising candidate ground states for the quantum antiferromagnetic Heisenberg model on the Kagome lattice is the valence bond solid (VBS) with a 36-site unit cell. We present a theory of triplet excitation spectra about this ground state using bond operator formalism. In particular we obtain dispersions of all 18 triplet modes in the reduced Brillouin zone. In the bond operator mean-field theory, it is found that a large number of triplet modes are non-dispersive. In particular, the lowest triplet excitation is non-dispersive and degenerate with a dispersive mode at the zone center. Away from the zone center, the lowest triplet is separated from two other flat modes by a small energy gap. Quantum fluctuations are considered by taking into account scattering processes of two triplets and their bound state formation, which leads to a downward renormalization of the lowest spin triplet gap. The dispersion of the lowest triplet excitation in the VBS state is compared with the dispersive lower bound of the triplet continuum expected in competing spin liquid phases. Implications to future neutron scattering experiments are discussed.