Strongly interacting fermions

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 $F_1^s$→∞. Some of the large $m^{\mathrm{*}}$ originate from a large ‘‘dynamic’’ mass, $m_{\lambda }$ 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 $F_0^s$,$F_1^s$→∞, 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.