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arXiv · 0707.0892

Ground State of the Kagome Lattice Heisenberg Antiferromagnet

Rajiv R. P. Singh·David A. Huse
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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'.

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Rajiv R. P. Singh, David A. Huse. 2008-01-08. Ground State of the Kagome Lattice Heisenberg Antiferromagnet. https://doi.org/10.1103/physrevb.76.180407

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