Collective density fluctuations of strange metals with critical Fermi surfaces

Recent spectroscopic measurements in a number of strongly correlated metals that exhibit non-Fermi liquid like properties have observed evidence anomalous frequency and momentum-dependent charge-density fluctuations. Specifically, the strange metallic regime cuprate superconductors, there is featureless particle-hole continuum exhibiting unusual power-laws, experiments suggest plasmon mode decays into this manner distinct from expectations conventional Fermi theory. Inspired by these new experimental developments, we address nature low-energy collective modes continua for different "solvable" lattice models liquids host critical surface -- sharp electronic without any quasiparticles. We scrutinize theoretically possible existence long-lived zero-sound mode, which renormalized to plasma presence long-ranged coulomb interactions, its decay over wide range frequencies momenta. Quite remarkably, some analyzed here can account certain aspects universal observations, clearly lie beyond purview standard