Point-like spin-dependent interaction in calculations of self-energy ladder diagrams

TL;DR

This paper introduces a zero-range, spin-dependent interaction model derived from ladder diagrams, analyzing its behavior across electron densities and spin polarizations, with an implementation using a Yukawa-type potential.

Contribution

It presents a novel zero-range spin-dependent interaction derived from ladder diagrams and provides an implementation with a Yukawa-type potential considering spin polarization.

Findings

Interaction strength varies with electron density and spin polarization.

The model captures uncorrelated electron-hole pair motions in singlet and triplet states.

Implementation demonstrates the feasibility of the proposed interaction model.

Abstract

An instantaneous and zero-range spin-dependent interaction, derived by summing an infinite number of electron-hole ladder diagrams within a local approximation, is analyzed as a function of the electron gas density and the relative spin polarization. The strength of such an interaction is defined by an integral of a statically screened Coulomb interaction with a spatially localized weighting factor. This weighting factor represents the mutually uncorrelated motion of an electron-hole pair in singlet or triplet spin states ($S^z=0,\pm1$). An implementation, based on a Yukawa-type interaction with a spin-polarization-dependent Thomas-Fermi screening length, is given.