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

Abstract

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.