Charge collective modes in strongly correlated electron systems with long range interactions

Elucidating the impact of strong electronic correlations on the collective modes of metallic systems has been of longstanding interest, mainly due to the inadequacy of the random phase approximation (RPA) in the strongly correlated regime. In his regard, we analyze the charge excitation spectrum of a Hubbard model on the face centered cubic lattice, extended with long range interactions, in different coupling regimes ranging from uncorrelated to the metal-to-insulator transition at half filling. We argue that the slave boson representation introduced by Kotliar and Ruckenstein, when formulated in radial gauge, constitutes a suitable framework to carry out this endeavor, and we compare its results to conventional RPA as a benchmark. We focus on the influence of the local and long range couplings on the particle-hole excitation continuum and the quantum collective phenomena generically comprised in our spectra, and find numerous qualitative and quantitative discrepancies between our method and standard RPA in the intermediate-to-strong coupling regime. At the onset of the Mott transition, the plasmon gap is found to vanish, supporting a quasiparticle description of the mode.