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

TL;DR

This paper compares the slave-boson and X-boson methods for the periodic Anderson model, analyzing their behavior at different temperature regimes and revealing phase transitions and limitations of each approach.

Contribution

It provides a detailed comparison of the slave-boson and X-boson methods, highlighting their breakdown points and phase transition behavior in the Kondo and high-temperature limits.

Findings

Slave-boson breaks down at intermediate temperatures with Nf = Nc = Nt/2.

X-boson exhibits a phase transition from Kondo heavy fermion to local moment magnetic regime at low temperatures.

Comparison shows differences in low-temperature behavior of the two methods.

Abstract

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).