Mixed Charge-Spin Response Functions of an Arbitrarily Polarized Electron Gas

TL;DR

This paper proves that two mixed charge-spin response functions are equal in a spin-polarized electron gas using multiple theoretical approaches, highlighting symmetry considerations and approximations.

Contribution

It demonstrates the equality of mixed charge-spin response functions in a polarized electron gas through various theoretical methods and symmetry arguments.

Findings

Two mixed charge-spin response functions are equal when orbital effects are negligible.

The equality holds within a generalized STLS approximation.

Symmetry considerations ensure the responses coincide exactly.

Abstract

In this paper, using different approaches we demonstrate the equality of the two mixed charge-spin response functions of a spin-polarized electron gas when orbital effects are negligible. Within a generalized STLS approximation we show that the two mixed responses are equal. We also present arguments for the equality of the two dynamic responses by considering a symmetry of the effective screened interaction between two opposite spin electrons. Furthermore, using the reflection symmetry of the system and the fact that the hamiltonian is real we prove rigorously that the two responses coincide identically.