Triplet and Singlet Excitations in the Valence Bond Crystal Phase of Kagome Lattice Heisenberg Model

TL;DR

This paper investigates the low-energy triplet and singlet excitations in the Valence Bond Crystal phase of the Kagome Lattice Heisenberg Model, revealing small spin gaps and numerous bound states consistent with previous numerical results.

Contribution

It provides detailed calculations of triplet and singlet excitations in the VBC phase for both infinite and finite Kagome lattices, highlighting finite-size effects and bound state formations.

Findings

Lowest triplet spin gap ~0.08 J in infinite lattice

Finite-size spin gap ~0.2 J on 36-site cluster

Numerous bound states below the spin gap

Abstract

A proposed ground state for the Kagome Lattice Heisenberg Model (KLHM) consists of a Valence Bond Crystal (VBC) with a 36-site unit cell. We calculate the low-lying triplet and singlet excitations in the VBC phase for the infinite-lattice model and for the 36-site cluster. For the infinite lattice, the lowest triplet excitation is found to have a spin gap of approximately $0.08 \pm 0.02 J$ and a bandwidth of only about $0.01 J$. For the 36-site cluster, consisting of a single unit cell with periodic boundary conditions, there are substantial finite-size effects: the spin gap there is estimated to be approximately $0.2 J$, close to the exact diagonalization result of $0.164 J$. The triplet excitations attract one another and form many bound states in the spin-singlet channel. We find a large number of such bound states for the 36-site cluster, many of which appear to lie below the spin gap, again in agreement with the results from exact diagonalization.