Finite-Temperature Spin Exchange-Correlation Kernel of the Uniform Electron Gas

TL;DR

This paper computes the finite-temperature spin exchange-correlation kernel of the uniform electron gas using variational diagrammatic Monte Carlo, providing insights into spin response across different regimes relevant for warm dense matter.

Contribution

It presents the first-principles calculation of the finite-temperature spin XC kernel of the UEG across multiple regimes, connecting to zero-temperature parametrizations and revealing new features.

Findings

The spin XC kernel smoothly connects to zero-temperature parametrizations at low T.

Heating suppresses Fermi-surface spin correlations and weakens Stoner enhancement.

In the classical regime, the spin XC kernel becomes nearly local on the Fermi-momentum scale.

Abstract

The finite-temperature spin response of the uniform electron gas (UEG) is a fundamental reference for spin-polarized and magnetized electron liquids, including warm dense matter (WDM), yet it remains far less constrained than charge response. Using variational diagrammatic Monte Carlo, we compute the static spin exchange--correlation (XC) kernel $K_{xc}(q;T)$ of the unpolarized UEG at metallic densities across the quantum-degenerate, warm-dense, and classical regimes. The kernel connects smoothly to zero-temperature spin-response parametrizations at low temperature, while heating suppresses the Fermi-surface-scale spin-correlation structure and weakens the XC-driven Stoner enhancement. Its long-wavelength limit provides a direct response test of the spin stiffness implied by thermal local-spin-density-approximation (LSDA) parametrizations, showing low-temperature consistency while exposing a resolved warm-dense residual in current LSDA parametrizations. In the classical regime, the spin XC kernel becomes nearly local on the Fermi-momentum scale, in sharp contrast to the corresponding charge XC kernel. These results provide a first-principles basis for finite-temperature spin-response theory and magnetized WDM modeling.