The main idea behind the formulation of QDMs is that, if the spin gap is large, the spin degrees of freedom become confined in tightly bound singlet states which, in the extreme limit of a very large spin gap, extend only over distance scales of the order of nearest-neighbor sites of the lattice. Thus, in this extreme regime, the Hilbert space can be approximately identified (up to some important caveats[@rokhsar88]) with the coverings of the lattice by valence bonds or dimers.

Surprisingly, even at the level of the oversimplified picture offered by QDMs, the physics of doped Mott insulators remains poorly understood. In this paper we explore the phase diagrams, and the properties of their phases, of QDMs generalized to include interactions between dimers (or valence bonds), and between dimers and doped (charged) holes. Basic aspects of the physics of these models are reviewed in Ref.  and references therein.

Undoped QDMs have been studied more extensively and by now they are relatively well understood.[@read-sachdev91; @sachdev-read91; @moessner01a; @moessner02a; @fradkin04; @vishwanath04; @ardonne04] On bipartite lattices, their ground states show either long-range crystalline valence bond order of different sorts or are quantum critical,[@rokhsar88; @fradkin91; @moessner02a] while on non-bipartite lattices their ground states are 