Ground State of the Kagome Lattice Heisenberg Antiferromagnet

TL;DR

This paper uses series expansions to suggest that the ground state of the Kagome lattice Heisenberg antiferromagnet is a Valence Bond Crystal with a 36-site unit cell, characterized by specific energy and excitation properties.

Contribution

It provides a detailed series expansion analysis indicating the VBC ground state with a 36-site unit cell as the lowest energy configuration, with new insights into its structure and excitations.

Findings

Ground state is a Valence Bond Crystal with a 36-site unit cell.

Energy per site is approximately -0.433 J.

Lowest-energy triplet excitations are dispersionless and confined.

Abstract

Using series expansions around the dimer limit, we show that the ground state of the Heisenberg Antiferromagnet on the Kagome Lattice appears to be a Valence Bond Crystal (VBC) with a 36-site unit cell, and an energy per site of $E/J=-0.433\pm0.001$. It is a honeycomb lattice of `perfect hexagons' as discussed by Nikolic and Senthil. The energy difference between the ground state and other ordered states with the maximum number of `perfect hexagons', such as a stripe-ordered state, is of order $0.001 J$. The energy of the 36-site system with periodic boundary conditions is further lowered by an amount of $0.005\pm 0.001 J$, consistent with Exact Diagonalization. Every unit cell of the VBC has two singlet states whose degeneracy is not lifted to $6th$ order in the expansion. We estimate this energy difference to be smaller than $0.001 J$. Two leading orders of perturbation theory find the lowest-energy triplet excitations to be dispersionless and confined to the `perfect hexagons'.