Strongly interacting fermions

Abstract

It is shown that strongly interacting Fermi systems, such as $^{3}\mathrm{He}$, transition metals, and the heavy-fermion systems can be consistently described within the ``induced''-interaction Fermi-liquid formalism. The general limiting features of the model are considered. In agreement with the Gutzwiller (half-filled case) solution to the Hubbard model, there is a localization of excitations as ${F}_{0}^{s}$ and ${F}_{1}^{s}$\ensuremath{\rightarrow}\ensuremath{\infty}. Some of the large ${m}^{\mathrm{*}}$ originate from a large ``dynamic'' mass, ${m}_{\ensuremath{\lambda}}$ for f electrons, which is then shown to be further increased by many-body effects. In disagreement with the Gutzwiller solution in the half-filled case, but in agreement with the less-than-half-filled case, the compression modulus goes to a finite value as ${F}_{0}^{s}$,${F}_{1}^{s}$\ensuremath{\rightarrow}\ensuremath{\infty}, so that---in a jellium model---the Debye frequency ${\mathrm{FTHETA}}_{D}$ has a finite value. The implication of the spin-dependent parameter ${F}_{0}^{a}$ going to a finite limit are discussed. In particular, it is shown that ferromagnetic ordering cannot occur in the case of a short-ranged potential.