Construction of Wannier functions from the spectral moments of correlated electron systems

TL;DR

This paper introduces a method to construct generalized Wannier functions from spectral moments, enabling improved spectral feature representation and calculations like the anomalous Hall effect in correlated electron systems.

Contribution

It develops a framework for constructing maximally localized spectral moment Wannier functions from spectral moments, extending the applicability of Wannier functions in correlated electron systems.

Findings

Constructed MLSMWFs from the first four spectral moments.

Demonstrated the use of MLSMWFs to compute the anomalous Hall effect in fcc Ni.

Proposed extension to more than four moments for enhanced spectral accuracy.

Abstract

When the first four spectral moments are considered, spectral features missing in standard Kohn-Sham (KS) density-functional theory (DFT), such as upper and lower Hubbard bands, as well as spectral satellite peaks, can be described, and the bandwidths can be corrected. Therefore, we have devised a \textit{moment-functional based spectral density functional theory} (MFbSDFT) recently. However, many computational tools in theoretical solid state physics, such as the construction of maximally localized Wannier functions (MLWFs), have been developed for KS-DFT and require modifications if they are supposed to be used in MFbSDFT. Here, we show how generalized Wannier functions may be constructed from the first four spectral moment matrices. We call these functions \textit{maximally localized spectral moment Wannier functions} (MLSMWFs). We demonstrate how MLSMWFs may be used to compute the anomalous Hall effect (AHE) in fcc Ni by Wannier interpolation. More generally, MLSMWFs may be computed from the first $2P$ moments ($P=1,2,3,\dots$). Using more than 4 moments opens the perspective of reproducing all spectral features accurately in MFbSDFT.