New Model Hamiltonian for the Metal-Insulator Transition

With use of the symmetry properties of the half-filled single-band Hubbard Hamiltonian, there is derived an effective Hamiltonian on a decimated lattice in which the spin and charge operators occur explicitly. Being a generalization of the Blume-Emery-Griffiths Hamiltonian for ${\mathrm{He}}^3$-${\mathrm{He}}^4$ mixtures, this new statistical mechanical model permits one to give a preliminary discussion of the phase diagram of the correlated electron gas by establishing analogies with their results.