Pyrochlore Antiferromagnet: A Three-Dimensional Quantum Spin Liquid

The quantum pyrochlore antiferromagnet is studied by perturbative expansions and exact diagonalization of small clusters. We find that the ground state is a spin-liquid state: The spin-spin correlation functions decay exponentially with distance and the correlation length never exceeds the interatomic distance. The calculated magnetic neutron diffraction cross section is in very good agreement with experiments performed on $\mathrm{Y}\left(\mathrm{Sc}\right){\mathrm{Mn}}_2$. The low energy excitations are singlet-singlet ones, with a finite spin gap.