Theory of multicomponent Fermi liquid: General formulas for susceptibilities and applications to periodic Anderson models

We treat the multicomponent fermion system (MCFS) in which several distinct types of fermions interact and hybridize mutually. For the most general MCFS we reconstruct and unify the Fermi-liquid theory for the susceptibility: (a) We obtain the dynamical susceptibility χ(q,Ω) on the basis of the Kubo formula, in a form where the identity of the original local basis and its relation to the quasiparticle (qp) band basis are transparent; (b) we obtain the isothermal static uniform susceptibility ${\mathrm{\chi }}_{\mathit{T}}$ by Luttinger’s procedure; and then (c) we present the explicit identities showing that χ(q→0,Ω==0) coincides with ${\mathrm{\chi }}_{\mathit{T}}$, provided that the magnetization is conserved; in addition to the mathematical origin, we give a physical interpretation of the singular behavior of χ(q,Ω) for small (q,Ω). In the latter part of this paper, three kinds of periodic Anderson models (PAM’s) are considered as examples of MCFS’s: (i) the SU(N) PAM, (ii) a doubly degenerate PAM with different g values for the c and f electrons, and (iii) an orbitally degenerate PAM with different degeneracies for the c and f electrons. The qp and non-qp parts of the susceptibility are obtained separately, and we find that the non-qp parts of these models behave completely differently from each other. This diversity of the behavior of the non-qp parts depending on the details of the model suggests a possible resolution of the Wilson-ratio problem of the heavy-fermion systems posed by Anderson and others.