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arXiv · 1006.4299

Exact ground states for coupled spin trimers

Heinz-Jürgen Schmidt·Johannes Richter
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Abstract

We consider a class of geometrically frustrated Heisenberg spin systems which admit exact ground states. The systems consist of suitably coupled antiferromagnetic spin trimers with integer spin quantum numbers $s$ and their ground state $\Phi$ will be the product state of the local singlet ground states of the trimers. We provide linear equations for the inter-trimer coupling constants which are equivalent to $\Phi$ being an eigenstate of the corresponding Heisenberg Hamiltonian and sufficient conditions for $\Phi$ being a ground state. The classical case $s\to\infty$ can be completely analyzed. For the quantum case we consider a couple of examples, where the critical values of the inter-trimer couplings are numerically determined. These examples include chains of corner sharing tetrahedra as well as certain spin tubes. $\Phi$ is proven to be gapped in the case of trimer chains. This follows from a more general theorem on quantum chains with product ground states.

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Heinz-Jürgen Schmidt, Johannes Richter. 2010-06-22. Exact ground states for coupled spin trimers. https://doi.org/10.1088/1751-8113/43/40/405205

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