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

TL;DR

This paper develops a new computational method to accurately determine the exchange-correlation kernel in warm dense electron gases across various temperatures and momenta, revealing key physical behaviors and enabling improved density functional theory applications.

Contribution

A variational diagrammatic Monte Carlo method is introduced to compute the exchange-correlation kernel $K_{XC}(q;T)$ for warm dense matter, covering broad temperature and momentum ranges.

Findings

Identified temperature-dependent evolution of the hump structure and large-q tail in $K_{XC}$.

Derived an analytical form for $K_{XC}$ as $q o abla$, accurately capturing large-q tails.

Demonstrated the transformation of $K_{XC}$ data into real space for use in density functional theory.

Abstract

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