Study of the Kondo and high-temperature limits of the slave-boson and X-boson methods

In this Letter we study the periodic Anderson model, employing both the slave-boson and the X-boson approaches in the mean field approximation. We investigate the breakdown of the slave-boson at intermediate temperatures when the total occupation number of particles Nt=Nf+Nc is keep constant, where Nf and Nc are respectively the occupation numbers of the localized and conduction electrons, and we show that the high-temperature limit of the slave-boson is Nf=Nc=Nt/2. We also compare the results of the two approaches in the Kondo limit and we show that at low-temperatures the X-boson exhibits a phase transition, from the Kondo heavy fermion (K-HF) regime to a local moment magnetic regime (LMM).