Kagome´ spin-1/2 antiferromagnets in the hyperbolic plane

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Abstract
Spin-dimerized states are useful in the construction of spin-disordered wave functions but difficult to deal with because of nonorthogonality. For the spin-1/2 kagome$aa— antiferromagnet, a systematic expansion of matrix elements of these nonorthogonal states is made possible by considering generalizations of the kagome$aa— structure in the hyperbolic plane. The first nontrivial term in this expansion is an effective spin Hamiltonian which describes resonance among dimerized states. Minimum-energy states of the effective Hamiltonian correspond to a high degree of resonance among a small fraction of the dimers.