Long wavelength behavior of the dynamical spin-resolved local-field factor in a two-dimensional electron liquid

TL;DR

This paper investigates the high-frequency behavior of the spin-resolved local-field factor in a two-dimensional electron liquid, revealing a logarithmic divergence and analyzing the static structure factor at large wavevectors.

Contribution

It provides a detailed analysis of the high-frequency limits and large wavevector structure of the spin-resolved local-field factor in 2D electron liquids, including divergence behavior.

Findings

Real part of A(ω) diverges logarithmically at large ω

Large wavevector structure of the static structure factor is characterized

High frequency limits of the spin-resolved exchange-correlation kernel are established

Abstract

The high frequency limits of the singular component $A(\omega)$ of the small wavevector expansion of the longitudinal (L) and transverse (T) components of the spin-resolved exchange-correlation kernel tensor $f_{xc,\sigma \sigma'}^{L,T}(q,\omega)=-v(q)G_{\sigma \sigma'}^{L,T}(q,\omega)$ in a two-dimensional isotropic electron liquid with arbitrary spin polarization are studied. Here $G_{\sigma \sigma'}^{L,T}(q,\omega)$ is the spin-resolved local field factor, $v(q)$ is the Coulomb interaction in momentum space, and $\sigma$ denotes spin. Particularly, the real part of $A(\omega)$ is found to be logarithmically divergent at large $\omega$. the large wavevetor structure of the corresponding spin-resolved static structure factor is also established.