What can Mott insulators teach us about density-functional theory (and vice versa)?

TL;DR

This paper investigates the Mott insulating phase of the 1D Hubbard model using a Bethe Ansatz-based local-density approximation, revealing the importance of derivative discontinuity for accurately predicting the Mott gap.

Contribution

It introduces a Bethe Ansatz-based LDA functional with an explicit derivative discontinuity, providing a more accurate description of the Mott gap in 1D systems.

Findings

BA-LDA correctly predicts the Mott gap regardless of correlation strength

Derived an analytical formula for the Mott gap in the thermodynamic limit

Discontinuity contribution to the gap exceeds band-structure effects in 1D systems

Abstract

We study the Mott insulating phase of the one-dimensional Hubbard model using a local-density approximation (LDA) that is based on the Bethe Ansatz (BA). Unlike conventional functionals, the BA-LDA has an explicit derivative discontinuity. We demonstrate that as a consequence of this discontinuity the BA-LDA yields the correct Mott gap, independently of the strength of the correlations. A convenient analytical formula for the Mott gap in the thermodynamic limit is also derived. We find that in one-dimensional quantum systems the contribution of the discontinuity to the full gap is more important than that of the band-structure gap, and discuss some consequences this finding has for electronic-structure calculations.