Exactly Solvable Model of Correlated Lattice Electrons in Any Dimensions

This is the authors' abstract. We don't add key points for this paper.

We present an exactly solvable Hamiltonian which consists of nearest neighbor hopping and long-range interaction. The ground state and the thermodynamic quantities are analytically obtained in any dimensions. In a repulsive case, the Luttinger's theorem breaks down and the hypothesis of the adiabatic continuation no longer holds. At half filling, we show the existence of a metal-insulator transition as a function of the strength of the interaction. The zero energy excitation disappears at the critical value of the interaction when we increase the interaction. In this case, the system is an insulator. The charge compressibility behaves as κ≈|1-ρ| 1-2/ d near half filling in d dimensions where ρ is the density of electrons. At other fillings, there is always a zero energy excitation and the system is metallic. When the interaction is attractive, the ground state is composed of pairs of electrons with opposite spins. The low energy excitations, however, is not a particle-hole type of a non-interacting case but a pairwise excitation across the Fermi surface.