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

Quantum Phase Transitions induced by Infinite Dilution in the Fock Space: a General Mechanism. Proof and discussion