The non-Fermi-liquid nature of the metallic states of the Hubbard Hamiltonian

We present a formalism which enables us to express, for arbitrary d, the behaviour of the momentum-distribution function n_{sigma}(k) pertaining to uniform metallic ground states of the single-band Hubbard Hamiltonian H close to S_{F;sigma} (the Fermi surface of the fermions with spin index sigma, sigma = uparrow,downarrow) in terms of a small number of constant parameters which are bound to satisfy certain inequalities implied by the requirement of the stability of the ground state of the system. These inequalities restrict the range of variation of n_{sigma}(k) for k infinitesimally inside and outside the Fermi sea pertaining to fermions with spin index sigma and consequently the range of variation of the zero-temperature limit of n_{sigma}(k) for k on S_{F;sigma}. On the basis of some available accurate numerical results for n_{sigma}(k) pertaining to the Hubbard and the t-J Hamiltonian, we conclude that, at least in the strong-coupling regime, the metallic ground states of H for d=2 cannot be Fermi-liquid, nor can they in general be purely Luttinger- or marginal-Fermi liquids. We further rigorously identify the pseudo-gap phenomenon, or `truncation' of the Fermi surface, clearly observed in the normal states of under-doped copper-oxide superconductors, as corresponding to a line of resonance energies located below the Fermi energy, with a concomitant suppression to zero of the jump in n_{sigma}(k) over the `truncated' parts of the Fermi surface. [Short Abstract]