Spin-density-functional theory: some open problems and application to inhomogeneous Heisenberg models

TL;DR

This paper discusses open problems in spin-density-functional theory (SDFT), explores its application to inhomogeneous Heisenberg models, and demonstrates that DFT can be an efficient alternative for studying such quantum spin systems.

Contribution

It introduces local-density approximations for the inhomogeneous Heisenberg model within SDFT and applies them to finite and impurity systems, showing practical computational benefits.

Findings

DFT can be adapted to Heisenberg models with suitable reinterpretation of density

Local-density approximations are effective for inhomogeneous spin systems

DFT provides a computationally efficient alternative to traditional statistical mechanics methods

Abstract

Spin-density-functional theory (SDFT) is the most widely implemented and applied formulation of density-functional theory. However, it is still finding novel applications, and occasionally encounters unexpected problems. In this paper we first briefly describe a few of the latter, related to issues such as nonuniqueness, noncollinearity, and currents. In the main part we then turn to an example of the former, namely SDFT for the Heisenberg model. It is shown that time-honored concepts of Coulomb DFT, such as the local-density approximation, can be applied to this (and other) model Hamiltonians, too, once the concept of 'density' has been suitably reinterpreted. Local-density-type approximations for the inhomogeneous Heisenberg model are constructed. Numerical applications to finite-size and impurity systems demonstrate that DFT is a computationally efficient and reasonably accurate alternative to conventional methods of statistical mechanics for the Heisenberg model.