Susceptibility for the degenerate Anderson model with a strong correlation

Norio Kawakami, Ayao Okiji

Valerii Vladimirovich Val'kov, Dmitrii Mikhailovich Dzebisashvili

Masahiro Nakano

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 \ensuremath{\chi}(q,\ensuremath{\Omega}) 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 ${\mathrm{\ensuremath{\chi}}}_{\mathit{T}}$ by Luttinger's procedure; and then (c) we present the explicit identities showing that \ensuremath{\chi}(q\ensuremath{\rightarrow}0,\ensuremath{\Omega}==0) coincides with ${\mathrm{\ensuremath{\chi}}}_{\mathit{T}}$, provided that the magnetization is conserved; in addition to the mathematical origin, we give a physical interpretation of the singular behavior of \ensuremath{\chi}(q,\ensuremath{\Omega}) for small (q,\ensuremath{\Omega}). 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.

K. B. Efetov, A.I. Lapkin

Bo-Bo Wei

We investigate quantum phase transitions in one-dimensional quantum disordered lattice models, the Anderson model and the Aubry-Andr\'e model, from the fidelity susceptibility approach. First, we find that the fidelity susceptibility and the generalized adiabatic susceptibility are maximum at the quantum critical points of the disordered models, through which one can locate the quantum critical point in disordered lattice models. Second, finite-size scaling analysis of the fidelity susceptibility and of the generalized adiabatic susceptibility show that the correlation length critical exponent and the dynamical critical exponent at the quantum critical point of the one-dimensional Anderson model are respectively 2/3 and 2 and of the Aubry-Andr\'e model are respectively 1 and 2.375. Thus the quantum phase transitions in the Anderson model and in the Aubry-Andr\'e model are of different universality classes. Because the fidelity susceptibility and the generalized adiabatic susceptibility are directly connected to the dynamical structure factor which are experimentally accessible in the linear response regime, the fidelity susceptibility in quantum disordered systems may be observed experimentally in the near future.

N. Grewe