  Precise calculations of dynamics in the homogeneous electron gas (jellium
model) are of fundamental importance for design and characterization of new
materials. We introduce a diagrammatic Monte Carlo technique based on
algorithmic Matsubara integration that allows us to compute frequency and
momentum resolved finite temperature response directly in the real frequency
domain using series of connected Feynman diagrams. The data for charge response
at moderate electron density are used to extract the frequency dependence of
the exchange-correlation kernel at finite momenta and temperature. These
results are as important for development of the time-dependent density
functional theory for materials dynamics as ground state energies are for the
density functional theory.
