  We prove that lattice quantum systems may undergo a first-order quantum phase
transition through a general mechanism which consists in an infinite dilution
of the states associated to (or, more in general, near to) the lowest energy
levels. The equation giving the critical point is derived and discussed at
several degrees of generalizations: given an infinitesimal portion of the Fock
space, i.e., the cavity space, and its complement, i.e., the reservoir space,
in the thermodynamic limit, a first-order quantum phase transition takes place
when the cavity and reservoir energies are equal. A comparison with some
particular exact solvable cases as, e.g., the Quantum Rem model, is made.
