Frustrated Electron Liquids in the Hubbard Model

Abstract

The ground state of the Hubbard model is studied within the constrained Hilbert space where no order parameter exists. The self-energy of electrons is decomposed into the single-site and multisite self-energies. The calculation of the single-site self-energy is mapped to a problem of self-consistently determining and solving the Anderson model. When an electron reservoir is explicitly considered, it is proved that the single-site self-energy for the ground state is that of a normal Fermi liquid even if the multisite self-energy is so anomalous that the ground state itself is not a normal Fermi liquid. Thus, the ground state is a normal Fermi liquid in the supreme single-site approximation (S 3 A). In the strong-coupling regime, the Fermi liquid is stabilized by the Kondo effect in the S 3 A and further stabilized by the Fock-type term of the superexchange interaction or the resonating-valence-bond (RVB) mechanism beyond the S 3 A. The stabilized Fermi liquid is frustrated as much as an RVB spin liquid in the Heisenberg model, and is a relevant unperturbed state that can be used to study a normal or anomalous Fermi liquid and an ordered state in the entire Hilbert space by the Kondo lattice theory. Even if multisite terms of higher order than the Fock-type term are considered, the ground state cannot be an insulator with a complete gap nor a Mott insulator. It can only be a gapless semiconductor even if the multisite self-energy is so anomalous that it is divergent at the chemical potential. A Mott insulator is only possible as a high-temperature phase.