Atomic levels and Hybridization function

Detailed Description

Atomic levels and hybridization function.

Compute the hybridziation function

\[ [ \Delta^{\sigma} ]_{m m'} = \omega -\tilde{\varepsilon} - G_{\mathrm{loc}}^{-1}(\omega) - \Sigma_{\mathrm{imp}}(\omega), \]

where \(\omega\) is a frequency, \(\tilde{\varepsilon}\) are the effective local levels of the impurity, and \(\Sigma_{\mathrm{imp}}\) is the impurity self-energy.

The effecitve local levels are defined as:

\[ \tilde{\varepsilon} = \varepsilon - \mu - \Sigma_{\mathrm{DC}}, \]

where \(\mu\) is the chemical potential and \(\Sigma_{\mathrm{DC}}\) is the double counting self-energy.

Functions
template<typename Mesh >
block_gf< Mesh, matrix_valued >	triqs::modest::hybridization (std::vector< nda::matrix< dcomplex > > const &epsilon_levels, block_gf< Mesh, matrix_valued > const &Gloc)
	Compute the hybridization function from the effective impurity levels and the local Green's function.
template<typename Mesh >
block_gf< Mesh, matrix_valued >	triqs::modest::hybridization (std::vector< nda::matrix< dcomplex > > const &epsilon_levels, block_gf< Mesh, matrix_valued > const &Gloc, block_gf< Mesh, matrix_valued > const &Sigma_dynamic, std::vector< nda::matrix< dcomplex > > const &Sigma_static)
	Compute the hybridization function from the effective impurity levels, the local Green's function, and the impurity self-energy.
nda::array< nda::matrix< dcomplex >, 2 >	triqs::modest::impurity_levels (one_body_elements_on_grid const &obe)
	Compute the local impurity levels from the single-particle dispersion.
nda::array< nda::matrix< dcomplex >, 2 >	triqs::modest::impurity_levels (one_body_elements_tb const &obe)
	Compute the atomic (impurity) levels from an obe.

Function Documentation

hybridization() [1/2]

template<typename Mesh >

block_gf< Mesh, matrix_valued > triqs::modest::hybridization	(	std::vector< nda::matrix< dcomplex > > const &	epsilon_levels,
		block_gf< Mesh, matrix_valued > const &	Gloc
	)

#include <triqs_modest/gloc_fixed_grid.hpp>

Compute the hybridization function from the effective impurity levels and the local Green's function.

Template Parameters

Mesh	The mesh type.

Parameters

epsilon_levels	The effective impurity levels.
Gloc	The local Green's function of the impurity.

Returns

Hybridization function \( \Delta \).

Definition at line 238 of file gloc_fixed_grid.hpp.

hybridization() [2/2]

template<typename Mesh >

block_gf< Mesh, matrix_valued > triqs::modest::hybridization	(	std::vector< nda::matrix< dcomplex > > const &	epsilon_levels,
		block_gf< Mesh, matrix_valued > const &	Gloc,
		block_gf< Mesh, matrix_valued > const &	Sigma_dynamic,
		std::vector< nda::matrix< dcomplex > > const &	Sigma_static
	)

#include <triqs_modest/gloc_fixed_grid.hpp>

Compute the hybridization function from the effective impurity levels, the local Green's function, and the impurity self-energy.

Template Parameters

Mesh	The mesh type.

Parameters

epsilon_levels	The effective impurity levels.
Gloc	The local Green's function of the impurity.
Sigma_dynamic	The frequency dependent part of the impurity self-energy.
Sigma_static	The static term of the impurity self-energy.

Returns

Hybridization function \( \Delta \).

Definition at line 213 of file gloc_fixed_grid.hpp.

impurity_levels() [1/2]

nda::array< nda::matrix< dcomplex >, 2 > triqs::modest::impurity_levels

(

one_body_elements_on_grid const &

obe

)

#include <triqs_modest/downfolding.cpp>

Compute the local impurity levels from the single-particle dispersion.

Compute the atomic (impurity) levels from an obe.

Parameters

obe	One-body elements.

Returns

Impurity levels stored in the format [n_atoms, n_sigma].

Definition at line 117 of file downfolding.cpp.

impurity_levels() [2/2]

nda::array< nda::matrix< dcomplex >, 2 > triqs::modest::impurity_levels

(

one_body_elements_tb const &

obe

)

#include <triqs_modest/obe_tb.cpp>

Compute the atomic (impurity) levels from an obe.

Parameters

obe	One-body elements.

Returns

Impurity levels stored in the format [n_atoms, n_sigma].

Definition at line 101 of file obe_tb.cpp.