Quantum dimer calculations on the spin-1/2kagome´ Heisenberg antiferromagnet

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Abstract
In analogy to the quantum dimer model on the square lattice introduced by Rokhsar and Kivelson, we identify the low-energy Hilbert space of the spin-1/2 kagomé Heisenberg antiferromagnet with the set of dimerized states (nearest-neighbor singlets) and derive an effective Hamiltonian which describes resonance and includes fluctuations into next-nearest-neighbor singlets. Complete diagonalization of this effective Hamiltonian for systems as large as 36 spins makes possible the study of the low-energy thermodynamics of this quantum antiferromagnet and strongly supports the double peak feature in the heat capacity.