Model hamiltonians in density functional theory

TL;DR

This paper discusses the use of model Hamiltonians in density functional theory, highlighting how different choices can simplify the many-electron problem while maintaining the ability to approximate the real system's properties.

Contribution

It introduces the idea of using alternative model Hamiltonians with the same form as the physical Hamiltonian to systematically reduce approximations in density functional theory.

Findings

Model Hamiltonians can be chosen to reproduce the exact density.

Using Hamiltonians with the same form as the physical one allows systematic approximation improvements.

The approach facilitates closer approximation to the real many-electron system.

Abstract

The formalism of Kohn and Sham uses a specific (model) hamiltonian which highly simplifies the many-electron problem to that of noninteracting fermions. The theorem of Hohenberg and Kohn tells us that, for a given ground state density, this hamiltonian is unique. In principle, this density can be chosen as that of the real, interacting system. To obtain the energy, or other properties of the real system, approximations are needed. Working with non interacting fermions is an important simplification, but it may be easier to produce approximations with different choices of the model hamiltonian. The feature that the exact density is (ideally) reproduced can be kept in the newly defined fictitious systems. Using model hamiltonians having the same form as the physical one, that is, being built of one- and two-body operators, allows to approach the physical hamiltonian arbitrarily close, and thus a systematic reduction of the approximations.