Plasmonic properties and correlation energies from a compact multipole representation of the dielectric response in 2D metals
Multipole-Padé approximants provide a compact representation of dynamical response functions in terms of a small number of collective modes. Here, we generalize this framework to incorporate momentum dependence across the full Brillouin zone of 2D metals by constructing a symmetry-conserving, anisotropic representation of the inverse dielectric function. This analytic form enables efficient and accurate evaluation of quantities involving dynamical screening, including spectral features and correlation energies. We construct such compact representations for a set of seven two dimensional metals spanning distinct electronic regimes, and show that a small number of dispersive plasmonic modes suffices to accurately describe the dielectric response across the full Brillouin zone, while also yielding accurate correlation energies. The proposed representation therefore establishes a direct bridge between {\it ab initio} calculations and analytical models of screening, opening new avenues for applications in condensed matter systems.