Charges play musical chairs on the pyrochlore lattice

We study a highly idealized model for quantum ``charge order'' phase transitions on a pyrochlore lattice, loosely motivated by observations of a ``valence skipping'' structure in vanadium spinels (K. Matsuno et al, PRL 90, 096404, 2003). The model maps onto a particular 3+1-dimensional compact quantum electrodynamics. We describe the transition in terms of a dual theory of monopole defect proliferation. The model gives rise to a number of degenerate low energy excitations which can condense in various patterns. Latest results will be presented.