# Iterated projected position algorithm for constructing exponentially localized generalized Wannier functions for periodic and nonperiodic insulators in two dimensions and higher

@article{Stubbs2020IteratedPP, title={Iterated projected position algorithm for constructing exponentially localized generalized Wannier functions for periodic and nonperiodic insulators in two dimensions and higher}, author={Kevin D. Stubbs and Alexander B. Watson and Jianfeng Lu}, journal={arXiv: Mathematical Physics}, year={2020} }

Localized bases play an important role in understanding electronic structure. In periodic insulators, a natural choice of localized basis is given by the Wannier functions which depend a choice of unitary transform known as a gauge transformation. Over the past few decades, there have been many works which have focused on optimizing the choice of gauge so that the corresponding Wannier functions are maximally localized or reflect some symmetry of the underlying system. In this work, we consider…

## 5 Citations

### Algebraic localization implies exponential localization in non-periodic insulators

- 2021

Physics

Exponentially-localized Wannier functions are a basis of the Fermi projection of a Hamiltonian consisting of functions which decay exponentially quickly in space. In two and three spatial dimensions,…

### Existence and Computation of Generalized Wannier Functions for Non-Periodic Systems in Two Dimensions and Higher

- 2022

Mathematics

Archive for Rational Mechanics and Analysis

This work identifies an assumption under which it is proved that ELWFs can be constructed as the eigenfunctions of a sequence of self-adjoint operators acting on the Fermi projection and numerically verifies that the construction yields ELWF in various cases where this assumption holds.

### Hamiltonian Transformation for Band Structure Calculations

- 2022

Physics

An accurate and parameter-free method, called Hamiltonian transformation (HT), is proposed, to calculate band structures in both density functional theory (DFT) and post-DFT calculations with plane-wave basis sets, and can be used to improve the accuracy of the WI for systems with entangled bands.

### Localization of Generalized Wannier Bases Implies Chern Triviality in Non-periodic Insulators

- 2022

Physics

Annales Henri Poincaré

We investigate the relation between the localization of generalized Wannier bases and the topological properties of two-dimensional gapped quantum systems of independent electrons in a disordered…

### Localised Module Frames and Wannier Bases from Groupoid Morita Equivalences

- 2021

Mathematics

Journal of Fourier Analysis and Applications

Following the operator algebraic approach to Gabor analysis, we construct frames of translates for the Hilbert space localisation of the Morita equivalence bimodule arising from a groupoid…

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