Antiferromagnetic quantum spins on the pyrochlore lattice

The ground state of the S = 1/2 Heisenberg antiferromagnet on the pyrochlor e lattice is theoretically investigated. Starting from the limit of isolate d tetrahedra, I include interactions between the tetrahedra and obtain an e ffective model for the spin-singlet ground state multiplet by third-order p erturbation. I determine its ground state using the mean-field approximatio n and find a dimerized state with a four-sublattice structure, which agrees with the proposal by Harris et al. I also discuss chirality correlations a nd spin correlations for this state.