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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

Maximally localized Wannier functions are widely used in electronic structure theory for analyses of bonding, electric polarization, orbital magnetization, and for interpolation. The state of the art method for their construction is based…

Materials Science · Physics 2015-12-02 Jamal I. Mustafa , Sinisa Coh , Marvin L. Cohen , Steven G. Louie

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

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

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

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

We report on the implementation of the Wannier Functions (WFs) formalism within the full-potential linearized augmented plane wave method (FLAPW), suitable for bulk, film and one-dimensional geometries. The details of the implementation, as…

Materials Science · Physics 2008-07-21 F. Freimuth , Y. Mokrousov , D. Wortmann , S. Heinze , S. Blügel

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

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 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

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

In Kohn-Sham electronic structure computations, wave functions have singularities at nuclear positions. Because of these singularities, plane-wave expansions give a poor approximation of the eigenfunctions. In conjunction with the use of…

Numerical Analysis · Mathematics 2023-01-02 Xavier Blanc , Eric Cancès , Mi-Song Dupuy

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…

Mathematical Physics · Physics 2021-02-24 Kevin D. Stubbs , Alexander B. Watson , Jianfeng Lu

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

In this work, we present a computationally efficient methodology that utilizes a local real-space formulation of the projector augmented wave (PAW) method discretized with a finite-element (FE) basis to enable accurate and large-scale…

Computational Physics · Physics 2025-01-03 Kartick Ramakrishnan , Sambit Das , Phani Motamarri

Wannier functions provide a localized representation of spectral subspaces of periodic Hamiltonians, and play an important role for interpreting and accelerating Hartree-Fock and Kohn-Sham density functional theory calculations in quantum…

Computational Physics · Physics 2018-01-29 Anil Damle , Antoine Levitt , Lin Lin

EPW (Electron-Phonon coupling using Wannier functions) is a program written in FORTRAN90 for calculating the electron-phonon coupling in periodic systems using density-functional perturbation theory and maximally-localized Wannier…

Other Condensed Matter · Physics 2015-05-19 Jesse Noffsinger , Feliciano Giustino , Brad D. Malone , Cheol-Hwan Park , Steven G. Louie , Marvin L. Cohen

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

The description of realistic strongly correlated systems has recently advanced through the combination of density functional theory in the local density approximation (LDA) and dynamical mean field theory (DMFT). This LDA+DMFT method is…

Strongly Correlated Electrons · Physics 2009-11-13 B. Amadon , F. Lechermann , A. Georges , F. Jollet , T. O. Wehling , A. I. Lichtenstein

We present an alternative formalism for calculating the maximally localized Wannier functions in crystalline solids, obtaining an expression which is extremely simple and general. In particular, our scheme is exactly invariant under…

Materials Science · Physics 2011-03-03 Massimiliano Stengel , Nicola A. Spaldin
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