Phenomenological theory of first- and second-order metal-insulator transitions at absolute zero

A phenomenological theory of metal-insulator transitions at T = 0 is set up in which the order parameter is the discontinuity q in the single-particle occupation probability at the Fermi surface. Applied to the case of the second-order metal-insulator transition in a half-filled Hubbard band, q is found to have a critical exponent of unity, and the relation to Gutzwiller's variational treatment is exposed. The enhancement of the spin susceptibility by the Hubbard interaction is also treated. The same phenomenology is then applied to jellium, where a first-order metal-insulator transition occurs when the conducting electron fluid crystallizes on to the Wigner lattice. The form of the spin susceptibility, chemical potential, and energy is given near to, but on the high-density side of, the transition.