Densities and Chemical Potentials

Detailed Description

Functions to calculate the total electron density of lattice Green's functions using different methods and methods for chemical potenital searching given a target density.

Functions
template<typename Mesh >
double	triqs::modest::density (one_body_elements_on_grid const &obe, double mu, block2_gf< Mesh, matrix_valued > const &Sigma_dynamic, nda::array< nda::matrix< dcomplex >, 2 > const &Sigma_static)
	Compute the density of the lattice Green's function with a self-energy using Woodbury.
template<typename Mesh >
double	triqs::modest::density (one_body_elements_tb const &obe, double mu, block2_gf< Mesh, matrix_valued > const &Sigma_dynamic, nda::array< nda::matrix< dcomplex >, 2 > const &Sigma_static, triqs::lattice::bz_int_options const &opt)
	Compute the density of the lattice Green's function with a self-energy.
template<typename Mesh >
double	triqs::modest::find_chemical_potential (double const target_density, one_body_elements_on_grid const &obe, block2_gf< Mesh, matrix_valued > const &Sigma_dynamic, nda::array< nda::matrix< dcomplex >, 2 > const &Sigma_static, std::string method="dichotomy", double precision=1.e-5, bool verbosity=true)
	Find the chemical potenital from the local Green's function and self-energy given a target density.
double	triqs::modest::find_chemical_potential (double const target_density, one_body_elements_on_grid const &obe, double beta, std::string method="dichotomy", double precision=1.e-5, bool verbosity=true)
	Find the chemical potenital from the local Green's function given a target density.
template<typename Mesh >
double	triqs::modest::find_chemical_potential (double const target_density, one_body_elements_tb const &obe, block2_gf< Mesh, matrix_valued > const &Sigma_dynamic, nda::array< nda::matrix< dcomplex >, 2 > const &Sigma_static, triqs::lattice::bz_int_options const &opt, std::string method="dichotomy", double precision=1.e-5, bool verbosity=true)
	Find the chemical potenital from the local Green's function and self-energy given a target density.
template<typename Mesh >
double	triqs::modest::find_chemical_potential (double const target_density, one_body_elements_tb const &obe, Mesh const &mesh, triqs::lattice::bz_int_options const &opt, std::string method="dichotomy", double precision=1.e-5, bool verbosity=true)
	Find the chemical potenital from the local Green's function and self-energy given a target density.

Function Documentation

density() [1/2]

template<typename Mesh >

double triqs::modest::density	(	one_body_elements_on_grid const &	obe,
		double	mu,
		block2_gf< Mesh, matrix_valued > const &	Sigma_dynamic,
		nda::array< nda::matrix< dcomplex >, 2 > const &	Sigma_static
	)

#include <triqs_modest/density.hpp>

Compute the density of the lattice Green's function with a self-energy using Woodbury.

Template Parameters

Mesh	The mesh type.

Parameters

obe	One-body elements.
mu	Chemical potential.
Sigma_dynamic	Dynamic part of the embedded self-energy.
Sigma_static	Static part of the embedded self-energy.

Returns

Electron density of the lattice Green's function.

Definition at line 93 of file density.hpp.

density() [2/2]

template<typename Mesh >

double triqs::modest::density	(	one_body_elements_tb const &	obe,
		double	mu,
		block2_gf< Mesh, matrix_valued > const &	Sigma_dynamic,
		nda::array< nda::matrix< dcomplex >, 2 > const &	Sigma_static,
		triqs::lattice::bz_int_options const &	opt
	)

#include <triqs_modest/obe_tb.hpp>

Compute the density of the lattice Green's function with a self-energy.

Template Parameters

Mesh	The mesh type.

Parameters

obe	One-body elements.
mu	Chemical potential.
Sigma_dynamic	Dynamic part of the embedded self-energy.
Sigma_static	Static part of the embedded self-energy.
opt	Container for options related to the integration of the BZ.

Returns

Electron density of the lattice Green's function.

Definition at line 188 of file obe_tb.hpp.

find_chemical_potential() [1/4]

template<typename Mesh >

double triqs::modest::find_chemical_potential	(	double const	target_density,
		one_body_elements_on_grid const &	obe,
		block2_gf< Mesh, matrix_valued > const &	Sigma_dynamic,
		nda::array< nda::matrix< dcomplex >, 2 > const &	Sigma_static,
		std::string	method = "dichotomy",
		double	precision = 1.e-5,
		bool	verbosity = true
	)

#include <triqs_modest/density.hpp>

Find the chemical potenital from the local Green's function and self-energy given a target density.

Template Parameters

Mesh	The mesh type.

Parameters

target_density	Total electron density.
obe	One-body elements.
Sigma_dynamic	Dynamic part of the embedded self-energy.
Sigma_static	Static part of the embedded self-energy.
method	Root finding method to use (default = dichotomy).
precision	Precision to end search (default = 1e-5).
verbosity	Printing of the root finder's progress (default = true).

Returns

Chemical potential corresponding to target density.

Definition at line 220 of file density.hpp.

find_chemical_potential() [2/4]

double triqs::modest::find_chemical_potential ( double const  target_density, one_body_elements_on_grid const &  obe, double  beta, std::string  method = "dichotomy", double  precision = 1.e-5, bool  verbosity = true  )

inline

#include <triqs_modest/density.hpp>

Find the chemical potenital from the local Green's function given a target density.

Parameters

target_density	Total electron density.
obe	One-body elements.
beta	Inverse temperature (units 1/eV).
method	Root finding method to use (default = dichotomy).
precision	Precision to end search (default = 1e-5).
verbosity	Printing of the root finder's progress (default = true).

Returns

Chemical potential corresponding to target density.

Definition at line 199 of file density.hpp.

find_chemical_potential() [3/4]

template<typename Mesh >

double triqs::modest::find_chemical_potential	(	double const	target_density,
		one_body_elements_tb const &	obe,
		block2_gf< Mesh, matrix_valued > const &	Sigma_dynamic,
		nda::array< nda::matrix< dcomplex >, 2 > const &	Sigma_static,
		triqs::lattice::bz_int_options const &	opt,
		std::string	method = "dichotomy",
		double	precision = 1.e-5,
		bool	verbosity = true
	)

#include <triqs_modest/obe_tb.hpp>

Find the chemical potenital from the local Green's function and self-energy given a target density.

Template Parameters

Mesh	The mesh type.

Parameters

target_density	Total electron density.
obe	One-body elements.
Sigma_dynamic	Dynamic part of the embedded self-energy.
Sigma_static	Static part of the embedded self-energy.
opt	Container for options related to integration of the BZ.
method	Root finding method to use (default = dichotomy).
precision	Precision to end search (default = 1e-5).
verbosity	Printing of the root finder's progress (default = true).

Returns

Chemical potential corresponding to target density.

Definition at line 220 of file obe_tb.hpp.

find_chemical_potential() [4/4]

template<typename Mesh >

double triqs::modest::find_chemical_potential	(	double const	target_density,
		one_body_elements_tb const &	obe,
		Mesh const &	mesh,
		triqs::lattice::bz_int_options const &	opt,
		std::string	method = "dichotomy",
		double	precision = 1.e-5,
		bool	verbosity = true
	)

#include <triqs_modest/obe_tb.hpp>

Find the chemical potenital from the local Green's function and self-energy given a target density.

Template Parameters

Mesh	The mesh type.

Parameters

target_density	Total electron density.
obe	One-body elements.
mesh	Mesh on which local GF will be computed.
opt	Container for options related to integration of the BZ.
method	Root finding method to use (default = dichotomy).
precision	Precision to end search (default = 1e-5).
verbosity	Printing of the root finder's progress (default = true).

Returns

Chemical potential corresponding to target density.

Definition at line 244 of file obe_tb.hpp.