On the (anisotropic) uniform metallic ground states of fermions interacting through arbitrary two-body potentials in d dimensions

Abstract

We demonstrate that the skeleton of the Fermi surface pertaining to a uniform metallic ground state (corresponding to fermions with spin index σ) is determined by the Hartree–Fock contribution to the dynamic self-energy . That is to say, in order for , it is necessary (but for anisotropic ground states in general not sufficient) that the following equation be satisfied: where stands for the underlying non-interacting energy dispersion and ϵF for the exact interacting Fermi energy. The Fermi surface consists of the set of k points which in addition to satisfying the above equation fulfil where1 The set of k points which satisfy the first of the above two equations but fail to satisfy the second constitute the pseudogap region of the putative Fermi surface of the interacting system. We consider the behaviour of the ground-state momentum distribution function for k in the vicinity of and show that, whereas for the uniform metallic ground states of the conventional single-band Hubbard Hamiltonian, described in terms of an on-site interaction, and (here and denote vectors infinitesimally close to , located respectively inside and outside the underlying Fermi sea), for interactions of non-zero range these inequalities can be violated (without thereby contravening the stability condition ). This aspect is borne out by the pertaining to the normal states of for instance liquid 3He (corresponding to a range of applied pressure) as determined by means of quantum Monte Carlo calculations. We further demonstrate that for Fermi-liquid metallic states of fermions interacting through interaction potentials of non-zero range (e.g. the Coulomb potential), the zero-temperature limit of does not need to be equal to ½ for ; this in strict contrast with the uniform Fermi-liquid metallic states of the single-band Hubbard Hamiltonian (if such states at all exist). This aspect should be taken into account while analysing the deduced from the angle-resolved photoemission data concerning real materials. We discuss, in the light of the findings of the present work, the growing experimental evidence with regard to the ‘frustration’ of the kinetic energy of the charge carriers in the normal states of the copper-oxide-based high-temperature superconducting compounds.