Density-functional treatment of model Hamiltonians: basic concepts and application to the Heisenberg model

TL;DR

This paper explores how density-functional theory can be applied to inhomogeneous Heisenberg models, providing a computationally efficient method that improves upon mean-field approximations for calculating ground-state energies.

Contribution

It introduces a density-functional approach tailored for the Heisenberg model and demonstrates its effectiveness through various inhomogeneous cases, highlighting its advantages over traditional methods.

Findings

Density-functional results significantly improve over mean-field approximations.

The method accurately captures effects of boundaries and impurities.

Computational cost remains low compared to exact diagonalization.

Abstract

We describe how density-functional theory, well-known for its many uses in ab initio calculations of electronic structure, can be used to study the ground state of inhomogeneous model Hamiltonians. The basic ideas and concepts are discussed for the particular case of the Heisenberg model. As representative applications, illustrating scope and limitations of the procedure, we calculate the ground-state energy of one-, two- and three-dimensional antiferromagnetic Heisenberg models in the presence of boundaries and of impurities in the bulk and at the surfaces. Correlations are shown to lift degeneracies present in the mean-field approximation. Comparison with exact (brute force) diagonalization shows that the density-functional results are a significant improvement over the mean-field ones, at negligible extra computational cost.