Scheme for generalized maximally localized Wannier functions in one dimension

TL;DR

This paper presents a simple, exact, and computationally efficient method for constructing maximally localized Wannier functions in one-dimensional periodic potentials, ensuring unique and optimal results for various physical applications.

Contribution

It introduces a novel, straightforward procedure for generating maximally localized Wannier functions in 1D, avoiding complex numerical minimization and guaranteeing consistent results.

Findings

Method guarantees unique and optimal Wannier functions

Enables efficient evaluation of Hubbard interactions and matrix elements

Simplifies the construction process for 1D periodic potentials

Abstract

Maximally localized Wannier functions are the key tool for a variety of physical applications of Bloch states. Here we develop a simple and exact procedure to construct maximally localized Wannier functions for one dimensional periodic potentials of arbitrary form. As opposed to relatively complex numerical minimization approaches that may return somewhat different results depending on implementation and running conditions, this computationally straightforward method guarantees a unique (and optimal) result on each run. These features make it a useful vehicle for evaluation of Hubbard interactions, overlaps and various matrix elements in a simple and efficient manner.