An unambiguous and robust formulation for Wannier localization

TL;DR

This paper introduces a new variational approach for Wannier localization that is continuous, consistent, and adaptable, improving robustness and efficiency in computing localized orbitals under periodic boundary conditions.

Contribution

It presents a novel variational definition for orbital spread under PBCs, addressing limitations of previous methods and enabling more robust Wannier function localization.

Findings

Achieves 10x-70x reduction in iterations for localization

Provides a continuous and gauge-invariant spread measure

Demonstrates effectiveness across various materials

Abstract

We provide a new variational definition for the spread of an orbital under periodic boundary conditions (PBCs) that is continuous with respect to the gauge, consistent in the thermodynamic limit, well-suited to diffuse orbitals, and systematically adaptable to schemes computing localized Wannier functions. Existing definitions do not satisfy all these desiderata, partly because they depend on an "orbital center"-an ill-defined concept under PBCs. Based on this theoretical development, we showcase a robust and efficient (10x-70x fewer iterations) localization scheme across a range of materials.