Path-Integral Treatment for Localized Electrons in the Periodic Anderson Model

The partition function of the periodic Anderson model is presented as the path integral over the variables of "slow" localized d-electrons and of "light" conduction s-electrons with the energy half-bandwidth w. The adiabatic approximation is applied for d-electrons with level E<0 through the averaging of the thermal distribution over the "light" s-electron trajectories. The conditions are deduced for the temperature and for the relative positions of s- and d-electron levels, that prove this approximation. Temperature minimum of the effective one-particle d-electron energy with the corresponding maximum of their density of states follow for high temperature and the shallow d-level |E|<w, while the energy shift δ E(T) demonstrates the Kondo-like temperature logarithm. The Hubbard-like behaviour of d-electrons is found for deep level |E|>w and low temperatures.