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

TL;DR

This paper develops a formalism to analyze the momentum distribution in Hubbard model ground states, revealing that in two dimensions, these states are non-Fermi-liquid and relate to pseudogap phenomena in cuprates.

Contribution

It introduces a formalism for describing the momentum distribution near the Fermi surface in Hubbard models, linking non-Fermi-liquid behavior to pseudogap features in high-temperature superconductors.

Findings

Metallic states in 2D Hubbard model are non-Fermi-liquid.

Pseudo-gap phenomena correspond to resonance energies below the Fermi level.

Fermi surface truncation is associated with zero jump in n_sigma(k).

Abstract

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]