on a pyrochlore lattice.
The ground state of the antiferromagnetic Heisenberg model on a pyrochlore lattice is a gapped spin liquid (see this PRB by Canals and Lacroix). The ground state consists of weakly coupled RVB (resonating valence bond) states on each tetrahedra. The conditions necessary for deconfined spinons has been explored in Klein type models on the pyrochlore lattice.
The material KOs2O6 has a pyrochlore structure and was discovered to be superconducting with a transition temperature of about 10 K. Originally it was thought (and hoped) that the superconductivity might be intimately connected to RVB physics. However, it now seems that the superconductivity is not unconventional. It can be explained in terms of strong coupling electron-phonon interaction which arises because of anharmonic phonons associated with ``rattling" vibrational modes of the K ions which are located inside relatively large spatial regions within the cage of Os and O ions (see this paper).
To me this is a cautionary tale in my enthusiasm for RVB physics.