Exact Kohn-Sham Density Functional Theory on a Lattice

TL;DR

This paper presents an exact numerical method for solving the Kohn-Sham equations on a lattice, specifically applied to a finite Hubbard chain, enabling precise determination of the potential and energy components.

Contribution

It introduces a novel self-consistent cycle approach that maps the non-interacting Kohn-Sham wavefunction to the exact interacting wavefunction without referencing the latter directly.

Findings

Exact Kohn-Sham potential and energies obtained for the Hubbard chain

Self-consistent cycles successfully converge to the exact density and potential

Method provides a benchmark for density functional theory on lattices

Abstract

We formulate a set of equations that facilitate an exact numerical solution of the Kohn-Sham potential for a finite Hubbard chain with nearest neighbour hopping and arbitrary site potentials. The approach relies on a mapping of the non-interacting Kohn-Sham ground state wave function onto the exact interacting system wavefunction and two interconnected self-consistent cycles. The self-consistent cycles are performed within the framework of the Kohn-Sham non-interacting system without any direct reference to the interacting system. The first self-consistent cycle updates the mapping of the non-interacting wavefunction onto the interacting wavefunction based on a trial input density, while the second self-consistent cycle updates the Kohn-Sham potential to yield the trial density. At the solution point, the exact density, the exact Kohn-Sham potential, the density functional correlation energy and the exact interacting system ground state energy are available.