Strong correlations in density-functional theory: A model of spin-charge and spin-orbital separations

TL;DR

This paper explores the fractionalization of electrons into spinons, chargons, and orbitons within density-functional theory, revealing how these phenomena influence the behavior of Kohn-Sham eigenvalues and exchange-correlation potential discontinuities in strongly correlated systems.

Contribution

It introduces a model considering spin-charge and spin-orbital separations and analyzes their effects on exchange-correlation functionals in one-dimensional systems.

Findings

Spin-charge separation leads to nearly constant highest occupied Kohn-Sham eigenvalues.

Spin-orbital separation significantly impacts the derivative discontinuities at strong correlations.

The model provides insights into electron fractionalization effects in density-functional theory.

Abstract

It is known that the separation of electrons into spinons and chargons, the spin-charge separation, plays a decisive role when describing strongly correlated density distributions in one dimension. In this manuscript, we extend the investigation by considering a model for the third electron fractionalization: the separation into spinons, chargons and orbitons -- the last associated with the electronic orbital degree of freedom. Specifically, we deal with two exact constraints of exchange-correlation (XC) density-functionals: (i) The constancy of the highest occupied (HO) Kohn-Sham (KS) eigenvalues upon fractional electron numbers, and (ii) their discontinuities at integers. By means of one-dimensional (1D) discrete Hubbard chains and 1D Hydrogen molecules in the continuum, we find that spin-charge separation yields almost constant HO KS eigenvalues, whereas the spin-orbital counterpart can be decisive when describing derivative discontinuities of XC potentials at strong correlations.