Exchange-correlation effect in the charge response of a warm dense electron gas

The study of warm dense matter, widely existing in nature and laboratories, is challenging due to the interplay quantum classical fluctuations. We develop a variational diagrammatic Monte Carlo method determine exchange-correlation kernel $K_{\rm XC}(q;T)$ electron gas for broad range temperature $T$ momentum $q$. observe several interesting physics, including $T$-dependent evolution hump structure large-$q$ tail emergence scaling relation. Particularly, by deriving an analytical form $q \to \infty$, we obtain tails XC}$ with high precision. It shown that data can be reliably transformed into real space, which directly used density-functional-theory calculations matter.