Valence transition in the periodic Anderson model

TL;DR

This paper demonstrates that the valence transition observed in CeCu$_{2}$Si$_{2}$ under high pressure can be explained using the periodic Anderson model and a novel projector-based renormalization method, revealing a breakdown of mixed valence and Fermi surface collapse.

Contribution

It introduces a sophisticated PRM approach to the periodic Anderson model that captures both mixed and integral valence solutions, advancing understanding of valence transitions in heavy fermion systems.

Findings

Valence transition explained by the periodic Anderson model.

Breakdown of mixed-valence state with f occupation change.

Potential Fermi surface collapse in heavy fermion state.

Abstract

A very rich phase diagram has recently been found in CeCu$_{2}$Si$_{2}$ from high pressure experiments where, in particular, a transition between an intermediate valence configuration and an integral valent heavy fermion state has been observed. We show that such a valence transition can be understood in the framework of the periodic Anderson model. In particular, our results show a breakdown of a mixed-valence state which is accompanied by a drastic change in the \textit{f} occupation in agreement with experiment. This valence transition can possibly be interpreted as a collapse of the large Fermi surface of the heavy fermion state which incorporates not only the conduction electrons but also the localized \textit{f} electrons. The theoretical approach used in this paper is based on the novel projector-based renormalization method (PRM). With respect to the periodic Anderson model, the method was before only employed in combination with the basic approximations of the well-known slave-boson mean-field theory. In this paper, the PRM treatment is performed in a more sophisticated manner where both mixed as well as integral valent solutions have been obtained. Furthermore, we argue that the presented PRM approach might be a promising starting point to study the competing interactions in CeCu$_{2}$Si$_{2}$ and related compounds.