Numerical Study of the Periodic Anderson Model with Holstein Phonons for the Description of Cerium Volume Collapse

Abstract

The volume collapse transition of Cerium has intrigued physicists since its discovery several decades ago. Various models and mechanisms have been proposed, the most prominent scenarios are based on the Mott transition and the Kondo volume collapse transition. In this study, we explore the volume collapse by a dynamical mean field theory (DMFT) study of the periodic Anderson model with electron-phonon coupling to the conduction band. This allows us to study the effect of the electron-phonon interaction on the volume collapse. In order to faithfully account for the volume collapse, we also include the effects due to the volume and temperature dependent bulk modulus. We find that as the electron-phonon interaction strength increases, the volume collapse effect is enhanced, which is consistent with the suggestion that the phonons have an important contribution in the volume collapse transition. Although we start with the canonical model for the Kondo volume collapse scenario, our results have some of the characteristics of the Mott scenario. For example, when we plot the conduction electron density of states, we find that when the electron-phonon interaction effect dominates over the Kondo effect in this system, the conduction band electron spectra develops a Mott gap at the Fermi energy. Moreover, the width of the gap is proportional to the effective electron-phonon interaction strength. Currently, we cannot determine the order of this Mott transition, however, we conjecture that the transition is continuous due to the fact that the phonon frequency in our model is pretty small, and the fact that the conduction electron is doped away from half filling, both of which tend to suppress a first order phase transition. The study of the two-particle quantities, such as the charge susceptibility and the magnetic susceptibility also reveals several interesting features of the system. From the behavior of the charge and magnetic susceptibilities and the electronic spectral functions, we can clearly see the competition between the electron-phonon interaction and the Kondo effect due to the hybridization between conduction electrons and localized impurity electrons.