  Quantum lattice systems are rigorously studied at low temperatures. When the
Hamiltonian of the system consists of a potential (diagonal) term and a - small
- off-diagonal matrix containing typically quantum effects, such as a hopping
matrix, we show that the latter creates an effective interaction between the
particles.
  In the case that the potential matrix has infinitely many degenerate ground
states, some of them may be stabilized by the effective potential. The low
temperature phase diagram is thus a small deformation of the zero temperature
phase diagram of the diagonal potential and the effective potential. As
illustrations we discuss the asymmetric Hubbard model and the hard-core
Bose-Hubbard model.
