Models of interacting bosons with exact ground states: a unified approach

We define an infinite class of ``frustration-free'' interacting lattice quantum Hamiltonians for bosons, constructed such that their exact ground states have a density distribution specified by the Boltzmann weight of a corresponding classical lattice gas problem. By appropriately choosing the classical weights, we obtain boson representations of various known solvable models, including quantum dimer and vertex models, toric code, and certain Levin-Wen string-net models. We also systematically construct solvable models with other interesting ground states, including ``quantum spin liquids,'' supersolids, ``Bose-Einstein insulators,'' Bose liquids with ``Bose surfaces'', and Bose-Einstein condensates that permit adiabatic evolution from a non-interacting limit to a Gutzwiller-projected limit.