The Role of the Kondo and Phonon Correlations in the Cerium Volume Collapse*

We review the most recent experimental and theoretical progress of the $\alpha \leftrightarrow \gamma$ volume collapse occurring in the element cerium. We discuss the experimental results which have been important in differentiating the various electronic and phononic properties of the volume collapse of cerium, these experiments illustrate that drastically different electronic and phononic properties exist between the small volume phase $\alpha$ and large volume phase $\gamma$ of cerium. After interpreting the physical data and realizing that the volume collapse in cerium is primarily the result of different electronic and vibronic correlations in the $\alpha$ and $\gamma$ phases we set up a Hamiltonian which encompasses the physical properties of the collapse. To model the electronic and phononic properties of the $\alpha \leftrightarrow \gamma$ transition of cerium we use the Periodic Anderson Model (PAM) + Holstein Model, with the aim that the Kondo like electronic correlations of the $\alpha$ phase is encoded in the PAM where the large vibronic physics of the $\gamma$ phase is encompassed in the Holstein Model which incorporates a conduction electron-phonon mediated interaction.