Model

The Model is a Julia struct that abstracts a single Wannierization, it contains all the necessary information for maximally localization of the crystal structure.

Model

Index

Wannier.Model
Wannier.Model
Wannier.Spread
Wannier.berry_connection
Wannier.center
Wannier.center
Wannier.center
Wannier.omega
Wannier.omega
Wannier.omega
Wannier.omega_grad
Wannier.omega_grad
Wannier.omega_local
Wannier.position_op
Wannier.position_op
Wannier.position_op
Wannier.rotate_gauge

Model

Wannier.Model — Type

struct Model

A struct containing the parameters and matrices of the crystal structure.

Fields

lattice: columns are the lattice vectors
atom_positions: columns are the fractional coordinates of atoms
atom_labels: labels of atoms
kgrid: number of kpoints along 3 lattice vectors
kpoints: columns are the fractional coordinates of kpoints
bvectors: bvectors satisfying the B1 condition
frozen_bands: indicates which bands are frozen
M: n_bands * n_bands * n_bvecs * n_kpts, overlap matrix $M_{\bm{k},\bm{b}}$
U: n_bands * n_wann * n_kpts, (semi-)unitary gauge rotation matrix $U_{\bm{k}}$
E: n_bands * n_kpts, energy eigenvalues $\epsilon_{n \bm{k}}$
recip_lattice: columns are the reciprocal lattice vectors
n_atoms: number of atoms
n_bands: number of bands
n_wann: number of wannier functions
n_kpts: number of kpoints
n_bvecs: number of bvectors

Note

This only cotains the necessary information for maximal localization. For Wannier interpolation, see InterpModel.

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Wannier.Model — Method

Model(lattice, atom_positions, atom_labels, kgrid, kpoints, bvectors, frozen_bands, M, U, E)

Construct a Model struct.

Arguments

lattice: columns are the lattice vectors
atom_positions: columns are the fractional coordinates of atoms
atom_labels: labels of atoms
kgrid: number of kpoints along 3 lattice vectors
kpoints: columns are the fractional coordinates of kpoints
bvectors: bvectors satisfying the B1 condition
frozen_bands: indicates which bands are frozen
M: n_bands * n_bands * n_bvecs * n_kpts, overlap matrix $M_{\bm{k},\bm{b}}$
U: n_bands * n_wann * n_kpts, (semi-)unitary gauge rotation matrix $U_{\bm{k}}$
E: n_bands * n_kpts, energy eigenvalues $\epsilon_{n \bm{k}}$

Tip

This is more user-friendly constructor, only necessary information is required. Remaining fields are generated automatically.

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Wannier.rotate_gauge — Method

rotate_gauge(model::Model, U::Array{T,3}; diag_H=false)

Rotate the gauge of a Model.

Arguments

model: a Model struct
U: n_bands * n_wann * n_kpts, (semi-)unitary gauge rotation matrix $U_{\bm{k}}$

Keyword Arguments

diag_H: if after rotation, the Hamiltonian is not diagonal, then diagonalize it and save the eigenvalues to model.E, and the inverse of the eigenvectors to model.U, so that the model is still in the input gauge U. Otherwise, if the rotated Hamiltonian is not diagonal, raise error.

Note

The original Model.U will be discarded; the M, and E matrices will be rotated by the input U. However, since E is not the Hamiltonian matrices but only the eigenvalues, if diag_H = false, this function only support rotations that keep the Hamiltonian in diagonal form.

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Spread

Wannier.Spread — Type

struct Spread

The Marzari-Vanderbilt (MV) spread functional.

From MV:

$\Omega = \sum_n \langle r^2 \rangle_n - | \langle r \rangle_n |^2$
$\langle r \rangle_n = -\frac{1}{N} \sum_{\bm{k},\bm{b}} w_{\bm{b}} \bm{b} \Im \log M_{nn}^{\bm{k},\bm{b}}$
$\langle r^2 \rangle_n = \frac{1}{N} \sum_{\bm{k},\bm{b}} w_{\bm{b}} \bm{b} \left[ \left( 1 - | M_{nn}^{\bm{k},\bm{b}} |^2 \right) + \left( \Im \log M_{nn}^{\bm{k},\bm{b}} \right)^2 \right]$

Fields