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We present a general method of constructing maximally localized Wannier functions. It consists of three steps: (1) picking a localized trial wave function, (2) performing a full band projection, and (3) orthonormalizing with the Lowdin…

Other Condensed Matter · Physics 2017-01-11 Junbo Zhu , Zhu Chen , Biao Wu

Since the seminal work of Marzari and Vanderbilt, maximally localized Wannier functions have become widely used as a real-space representation of the electronic structure of periodic materials. In this paper we introduce selectively…

Strongly Correlated Electrons · Physics 2016-04-08 Runzhi Wang , Emanuel A. Lazar , Hyowon Park , Andrew J. Millis , Chris A. Marianetti

We show that an optimized projection functions method can automatically construct maximally localized Wannier functions even for bands with nontrivial topology. We demonstrate this method on a tight-binding model of a two-dimensional…

Materials Science · Physics 2016-10-05 Jamal I. Mustafa , Sinisa Coh , Marvin L. Cohen , Steven G. Louie

We present a robust algorithm that computes (maximally localized) Wannier functions (WFs) without the need of providing an initial guess. Instead, a suitable starting point is constructed automatically from so-called local orbitals which…

Materials Science · Physics 2020-07-01 Sebastian Tillack , Andris Gulans , Claudia Draxl

We propose an algorithm to determine Maximally Localized Wannier Functions (MLWFs). This algorithm, based on recent theoretical developments, does not require any physical input such as initial guesses for the Wannier functions, unlike…

Materials Science · Physics 2017-03-13 Éric Cancès , Antoine Levitt , Gianluca Panati , Gabriel Stoltz

We present an automatized approach towards maximally localized Wannier functions (MLWFs) applicable to both occupied and unoccupied states. We overcome limitations of the standard optimized projection function (OPF) method and its…

Materials Science · Physics 2025-02-17 Sebastian Tillack , Claudia Draxl

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…

Strongly Correlated Electrons · Physics 2014-12-12 Yuri Lensky , Colin Kennedy

A procedure to construct symmetry-adapted Wannier functions in the framework of the maximally-localized Wannier function approach[Marzari and Vanderbilt, Phys. Rev. B \textbf{56}, 12847 (1997); Souza, Marzari, and Vanderbilt, \textit{ibid.}…

Strongly Correlated Electrons · Physics 2015-06-16 R. Sakuma

Maximally localized Wannier functions (MLWFs) are widely used to construct first-principles tight-binding models that accurately reproduce the electronic structure of materials. Recently, robust and automated approaches to generate these…

Computational Physics · Physics 2023-11-02 Junfeng Qiao , Giovanni Pizzi , Nicola Marzari

Maximally-localized Wannier functions are quantum wavefunctions resembling atomic orbitals that are used to describe electrons in condensed matter. Since their introduction in 1997, these functions have become ubiquitous in ab initio…

Computational Physics · Physics 2026-04-09 Sabyasachi Tiwari , Bruno Cucco , Viet-Anh Ha , Feliciano Giustino

Localized Wannier functions provide an efficient and intuitive means by which to compute dielectric properties from first principles. They are most commonly constructed in a post-processing step, following total-energy minimization.…

Materials Science · Physics 2012-05-16 David D. O'Regan , Mike C. Payne , Arash A. Mostofi

Maximally-localized Wannier functions (MLWFs) are widely employed as an essential tool for calculating the physical properties of materials due to their localized nature and computational efficiency. Projectability-disentangled Wannier…

Materials Science · Physics 2025-11-25 Yuhao Jiang , Junfeng Qiao , Nataliya Paulish , Weisheng Zhao , Nicola Marzari , Giovanni Pizzi

We report a theoretical scheme that enables the calculation of maximally localized Wannier functions in the formalism of projector-augmented-waves (PAW) which also includes the ultrasoft-pseudopotential (USPP) approach. We give a…

Soft Condensed Matter · Physics 2007-05-23 Andrea Ferretti , Arrigo Calzolari , Benedetta Bonferroni , Rosa Di Felice

Wannier functions that are maximally localized help in understanding many properties of crystalline materials. In the absence of topological obstructions, they are at least exponentially localized. In some cases such as flat-band…

Mesoscale and Nanoscale Physics · Physics 2021-07-30 Pratik Sathe , Fenner Harper , Rahul Roy

The maximally localized Wannier functions play a very important role in the study of chemical bonding, ballistic transport and strongly-correlated system, etc. A significant development in this branch was made in 1997 and conjectured that…

Materials Science · Physics 2014-07-28 Sangryol Ri , Suil Ri

Maximally localized Wannier functions are localized orthogonal functions that can accurately represent given Bloch eigenstates of a periodic system at a low computational cost, thanks to the small size of each orbital. Tight-binding models…

Materials Science · Physics 2019-03-15 Jae-Mo Lihm , Cheol-Hwan Park

We discuss a method for constructing generalized Wannier functions that are maximally localized at the minima of a one-dimensional periodic potential with a double-well per unit cell. By following the approach of (Marzari M and Vanderbilt D…

Quantum Gases · Physics 2013-07-04 Michele Modugno , Giulio Pettini

We present a method for obtaining well-localized Wannier-like functions (WFs) for energy bands that are attached to or mixed with other bands. The present scheme removes the limitation of the usual maximally-localized WFs method (N. Marzari…

Materials Science · Physics 2009-11-07 Ivo Souza , Nicola Marzari , David Vanderbilt

We use the maximally-localized Wannier function method to study bonding properties in amorphous silicon. This study represents, to our knowledge, the first application of the Wannier-function analysis to a disordered system. Our results…

Materials Science · Physics 2009-10-31 Pier Luigi Silvestrelli , Nicola Marzari , David Vanderbilt , Michele Parrinello

The electronic ground state of a periodic system is usually described in terms of extended Bloch orbitals, but an alternative representation in terms of localized "Wannier functions" was introduced by Gregory Wannier in 1937. The connection…

Materials Science · Physics 2012-11-28 Nicola Marzari , Arash A. Mostofi , Jonathan R. Yates , Ivo Souza , David Vanderbilt
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