Variational Formulation for Wannier Functions with Entangled Band Structure

@article{Damle2019VariationalFF,
  title={Variational Formulation for Wannier Functions with Entangled Band Structure},
  author={Anil Damle and Antoine Levitt and Lin Lin},
  journal={Multiscale Model. Simul.},
  year={2019},
  volume={17},
  pages={167-191}
}
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 physics and chemistry. For systems with isolated band structure, the existence of exponentially localized Wannier functions and numerical algorithms for finding them are well studied. In contrast, for systems with entangled band structure, Wannier functions… 
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References

SHOWING 1-10 OF 45 REFERENCES
Maximally localized Wannier functions for entangled energy bands
We present a method for obtaining well-localized Wannier-like functions (WF's) for energy bands that are attached to or mixed with other bands. The present scheme removes the limitation of the usual
Maximally-localized Wannier Functions: Theory and Applications
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
Maximally localized generalized Wannier functions for composite energy bands
We discuss a method for determining the optimally localized set of generalized Wannier functions associated with a set of Bloch bands in a crystalline solid. By ''generalized Wannier functions'' we
Spectral and Fermi surface properties from Wannier interpolation
We present an efficient first-principles approach for calculating Fermi surface averages and spectral properties of solids, and use it to compute the low-field Hall coefficient of several cubic
Compressed Representation of Kohn-Sham Orbitals via Selected Columns of the Density Matrix.
TLDR
This work presents a simple, robust, efficient, and highly parallelizable method to construct a set of optionally orthogonal, localized basis functions for the associated subspace, and demonstrates the numerical accuracy and parallel scalability of the SCDM procedure using orbitals generated by the Quantum ESPRESSO software package.
An updated version of wannier90: A tool for obtaining maximally-localised Wannier functions
TLDR
An updated version of wannier90 is presented, wannIER90 2.0, including minor bug fixes and parallel (MPI) execution for band-structure interpolation and the calculation of properties such as density of states, Berry curvature and orbital magnetisation.
SCDM-k: Localized orbitals for solids via selected columns of the density matrix
TLDR
This work generalizes the SCDM method to Kohn-Sham density functional theory calculations with k-point sampling of the Brillouin zone, which is needed for more general electronic structure calculations for solids.
Locality properties and Wannier functions for interacting systems
Abstract We define Wannier functions for interacting systems, and show that the results on the localization of the Wannier functions for non-interacting systems carry over to the Wannier functions
Compressed modes for variational problems in mathematics and physics
TLDR
This article describes a general formalism for obtaining spatially localized solutions to a class of problems in mathematical physics, which can be recast as variational optimization problems, such as the important case of Schrödinger’s equation in quantum mechanics.
Localised Wannier Functions in Metallic Systems
The existence and construction of exponentially localised Wannier functions for insulators are a well-studied problem. In comparison, the case of metallic systems has been much less explored, even
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