pengwann.descriptors.DescriptorCalculator.get_density_matrix_element

descriptors.DescriptorCalculator.get_density_matrix_element(c_star, c)

Calculate an element of the Wannier density matrix.

Parameters:

c_starndarray of complex

The complex conjugate of the coefficient matrix for Wannier function i with Bravais lattice vector R_1.

cndarray of complex

The coefficient matrix for Wannier function j with Bravais lattice vector R_2.

Returns:

elementcomplex

An element of the Wannier density matrix.

See also

get_coefficient_matrix

pengwann.occupations.get_occupation_matrix

Notes

A given element of the Wannier density matrix is constructed as

\[P_{\alpha\beta} = \sum_{nk} w_{k}f_{nk}\left(C^{\alpha}_{nk}\right)^{*} C^{\beta}_{nk},\]

where \(\left(C^{\alpha}\right)^{*}\) and \(C^{\beta}\) refer to the c_star and c arguments, \(f\) is the occupation matrix and \(\{w_{k}\}\) are k-point weights.