X-boson cumulant approach to the periodic Anderson model

Abstract

The Periodic Anderson Model (PAM) can be studied in the infinite U limit by employing the Hubbard X operators to project out the unwanted states. We have already studied this problem employing the cumulant expansion with the hybridization as perturbation, but the probability conservation of the local states (completeness) is not usually satisfied when partial expansions like the Chain Approximation (CHA) are employed. Here we treat the problem by a technique inspired in the mean field approximation of Coleman's slave-bosons method, and we obtain a description that avoids the unwanted phase transition that appears in the mean-field slave-boson method both when the chemical potential is greater than the localized level Ef at low temperatures (T) and for all parameters at intermediate T.Comment: Submited to Physical Review B 14 pages, 17 eps figures inserted in the tex

Heavy-fermion superconductivity: AnX-boson treatment

“…4, and when it crosses the hybridization gap, the conducting electrons do not have the required energy to tunnel through the gap and the system becomes an insulator. Again, this result would not be obtained by the mean-field slave boson method [15], since the approach breaks down in the Kondo region when N f → 1 and the upper band cannot be reached.…”

“…Since the thermodynamic potential was already calculated in detail by one of us and collaborators elsewhere [15] treating the hybridization Hamiltonian H V as an external perturbation, we shall just briefly outline its solution below. According to the λ parameter integration…”

Phase evolution of the electronic transmission through a Kondo correlated quantum dot

“…As we analyzed in our previous works [13,14], the impurity X-boson approach is not a reliable approximation, at very low temperatures, in the extreme Kondo regime but it is a good approximation, at low temperatures, in the intermediate valence and empty dot regime. At temperatures T ≈ T K or higher, the impurity X-boson approach is a good alternative to the SBMFT in all the regimes, because the SBMFT presents a spurious second order phase transition at T K [17], whereas the X-boson solution evolves to the correct thermodynamic limit at high temperatures [13].…”

“…These GF's are obtained by the X-boson approach [13,14]. The effective hybridization parameter is obtained by Γ e f f = Γ/(1 + x 2 ), with Γ = 2πρ c V 2 .…”

“…The effective hybridization parameter is obtained by Γ e f f = Γ/(1 + x 2 ), with Γ = 2πρ c V 2 . In our approximation we employ the local GF for the QD, obtained using the X-boson treatment for the impurity case [13,14].…”