Dynamic response of the homogeneous electron gas

To predict functional behavior of new materials, the knowledge of their dynamic response functions at finite temperature is of fundamental importance. In this context, the homogeneous electron gas (jellium) model plays a special role both as a paradigmatic system for understanding the physics of the electron liquid in solids as well as being the key element in the formulation of the time-dependent density functional theory (TDDFT). Here we introduce a diagrammatic Monte Carlo technique based on algorithmic Matsubara integration that allows us to compute frequency and momentum resolved finite temperature responses directly in the real frequency domain using series of connected Feynman diagrams. Using the obtained data for charge response at moderate electron density we for the first time computed the exchange-correlation kernel for jellium by a controlled method and revealed unexpected features in its frequency dependence, which should spark the development of better kernels for TDDFT both at zero and finite temperature.