Effective interactions due to quantum fluctuations

A class of quantum lattice models is considered, with Hamiltonians consisti ng of a classical (diagonal) part and a small off-diagonal part (e.g. hoppi ng terms), In some cases when the classical part has an infinite degeneracy of ground states, the quantum perturbation may stabilize some of them. The mechanism of this stabilization stems from effective potential created by the quantum perturbation. Conditions are found when this strategy can be rigorously controlled and th e low temperature phase diagram of the full quantum model can be proven to be a small deformation of the zero temperature phase diagram of the classic al part with the effective potential added. As illustrations we discuss the asymmetric Hubbard model and the Bose-Hubbard model.