  This work presents a many-fermion Hamiltonian with the following properties:
1) is exactly solvable, 2) has a second order insulator-metal quantum phase
transition, 3) has a well defined mean field approximation and 4) its
mean-field ground state displays a liquid-solid transition. The phenomenon of
symmetry breaking in fermionic self-consistent models is discussed in the light
of these remarkable properties of the many-body model.
