Fluctuation effects on the mean-field approximation in the slave boson method for the Anderson lattice

Applicability of the mean-field approximation is examined, when the slave boson technique is used for SU(N d ) Anderson lattice model. The fluctuation component of the slave boson field is explicitly introduced and its interactions with electrons are studied. The self-energy parts are calculated up to the second order of the interactions without relying upon the usual 1/N d -expansion rule. Using perturbed propagators, the author obtains modified self-consistency equations for the mean-field parameters. They are solved at the transition temperature and also at zero temperature. The transition temperature decreases by a certain factor when the fluctuation is incorporated. This factor mainly depends on the location of the atomic f level and the degeneracy N d . The author newly adopts this quantity as the quantitative measure of the fluctuation effects. It is confirmed that the mean-field theory is less affected by the fluctuation if the system is in the Kondo limit and the degeneracy is large. It is found that the fluctuation becomes more effective as the location of the atomic f level is closer to the Fermi level or the degeneracy of the orbital is smaller. The consequences for application of the mean-field theory to the real heavy-fermion compounds are discussed.