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

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 ɛF 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 <artwork name="TPHM101939eu2"> where <artwork name="TPHM101939eu3"> 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 <artwork name="TPHM101939ei7"> for k in the vicinity of <artwork name="TPHM101939ei8"> 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, <artwork name="TPHM101939ei9"> and <artwork name="TPHM101939ei10"> (here <artwork name="TPHM101939ei11"> and <artwork name="TPHM101939ei12"> denote vectors infinitesimally close to <artwork name="TPHM101939ei13">, 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 <artwork name="TPHM101939ei14">). This aspect is borne out by the <artwork name="TPHM101939ei15"> 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 <artwork name="TPHM101939ei16"> does not need to be equal to ½ for <artwork name="TPHM101939ei17">; 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 <artwork name="TPHM101939ei18"> 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.