Density functional theory with adaptive pair density

TL;DR

This paper introduces an adaptive density functional for interacting particles that adjusts both density and pair density, demonstrated through an exact functional for the inhomogeneous Hubbard model, improving upon local density approximation.

Contribution

It presents a novel density functional framework that adapts to inhomogeneous potentials, with an exact formulation for the Hubbard model and a practical approximation enhancing existing methods.

Findings

Functional form matches Gutzwiller approximation with an unknown factor

Approximation based on uniform problem solution improves accuracy

Significant enhancement over local density approximation

Abstract

We propose a density functional to find the ground state energy and density of interacting particles, where both the density and the pair density can adjust in the presence of an inhomogeneous potential. As a proof of principle we formulate an a priori exact functional for the inhomogeneous Hubbard model. The functional has the same form as the Gutzwiller approximation but with an unknown kinetic energy reduction factor. An approximation to the functional based on the exact solution of the uniform problem leads to a substantial improvement over the local density approximation.