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.

• Received 23 November 1992

DOI:https://doi.org/10.1103/PhysRevB.48.13647