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

Abstract

It has long since been argued that the metallic states of the single-band Hubbard Hamiltonian Ĥ in two spatial dimensions (i.e. for d = 2) should be non-Fermi liquid, a possibility that would lead to the understanding of the observed anomalous behaviour of the doped copper-oxide-based superconducting compounds in their normal metallic states. Here we present a formalism which enables us to express, for arbitrary d, the behaviour of the momentum-distribution function nσ(k) pertaining to uniform metallic ground states of Ĥ close to S F; σ (the Fermi surface of the fermions with spin index σ, σ = ↑, ↓) 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 in nσ(k) for k infinitesimally inside and outside the Fermi sea pertaining to fermions with spin index σ and consequently the range of variation in the zero-temperature limit of nσ(k) for k on S F; σ On the basis of some available accurate numerical results for nσ(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 Ĥ for d = 2 cannot be Fermi-liquid nor can they in general be purely Luttinger or marginal Fermi liquids. We further rigorously identify the pseudogap phenomenon, or 'truncation' of the Fermi surface, clearly observed in the normal states of underdoped copper-oxide-based superconductors, as corresponding to a line of resonance energies (i.e. these energies strictly do not relate to quasiparticles) located below the Fermi energy, with a concomitant suppression to zero of the jump in nσ(k) over the 'truncated' parts of the Fermi surface. Our analyses make explicit the singular significance of the non-interacting energy dispersion ε k underlying Ĥ in determining the low-energy spectral and transport properties of the metallic ground states of Ĥ.