Kinetic-Energy Density-Functional Theory on a Lattice

TL;DR

This paper develops a lattice kinetic-energy density-functional theory and a kinetic-energy Kohn-Sham scheme, demonstrating that including kinetic-energy density as a fundamental variable improves accuracy in modeling interacting systems.

Contribution

It introduces a novel lattice kinetic-energy density-functional framework with a corresponding keKS scheme, explicitly incorporating kinetic-energy density as a fundamental variable.

Findings

The approach establishes a one-to-one correspondence between external potentials and internal variables.

Constructs simple orbital-dependent functionals that outperform standard exchange-only Kohn-Sham approximations.

Self-consistent calculations show improved accuracy over traditional density-functional methods.

Abstract

We present a kinetic-energy density-functional theory and the corresponding kinetic-energy Kohn-Sham (keKS) scheme on a lattice and show that by including more observables explicitly in a density-functional approach already simple approximation strategies lead to very accurate results. Here we promote the kinetic-energy density to a fundamental variable along side the density and show for specific cases (analytically and numerically) that there is a one-to-one correspondence between the external pair of on-site potential and site-dependent hopping and the internal pair of density and kinetic-energy density. Based on this mapping we establish two unknown effective fields, the mean-field exchange-correlation potential and the mean-field exchange-correlation hopping, that force the keKS system to generate the same kinetic-energy density and density as the fully interacting one. We show, by a decomposition based on the equations of motions for the density and the kinetic-energy density, that we can construct simple orbital-dependent functionals that outperform the corresponding exact-exchange Kohn-Sham (KS) approximation of standard density-functional theory. We do so by considering the exact KS and keKS systems and compare the unknown correlation contributions as well as by comparing self-consistent calculations based on the mean-field exchange for the keKS and the exact-exchange for the KS system, respectively.