GF density

Detailed Description

Computation of the particle density from a Green's function.

Functions
template<typename BGf, int R> requires (is_block_gf_v<BGf>)
auto	triqs::gfs::density (BGf const &gin, std::vector< array< dcomplex, R > > const &known_moments)
	Compute the density block-wise from a block Green's function on a Matsubara or real-frequency mesh.
nda::matrix< dcomplex >	triqs::gfs::density (gf_const_view< mesh::imfreq > g, array_const_view< dcomplex, 3 > known_moments={})
	Compute the density from a Green's function.
dcomplex	triqs::gfs::density (gf_const_view< mesh::imfreq, scalar_valued > g, array_const_view< dcomplex, 1 > known_moments={})
	Compute the density from a Green's function.
nda::matrix< dcomplex >	triqs::gfs::density (gf_const_view< mesh::legendre > g)
	Compute the density from a Green's function.
dcomplex	triqs::gfs::density (gf_const_view< mesh::legendre, scalar_valued > g)
	Compute the density from a Green's function.
nda::matrix< dcomplex >	triqs::gfs::density (gf_const_view< mesh::refreq > g)
	Zero temperature density from integration on the real frequency axis.
nda::matrix< dcomplex >	triqs::gfs::density (gf_const_view< mesh::refreq > g, double beta)
	Finite temperature density from integration on the real frequency axis.
dcomplex	triqs::gfs::density (gf_const_view< mesh::refreq, scalar_valued > g)
	Compute the zero-temperature density from a real-frequency Green's function.
dcomplex	triqs::gfs::density (gf_const_view< mesh::refreq, scalar_valued > g, double beta)
	Compute the density from a Green's function.
auto	triqs::gfs::density (MemoryGf< mesh::dlr > auto const &g)
	Compute the density from a Green's function.
auto	triqs::gfs::density (MemoryGf< mesh::dlr_imfreq > auto const &g)
	Compute the density from a Green's function.
auto	triqs::gfs::density (MemoryGf< mesh::dlr_imtime > auto const &g)
	Compute the density from a Green's function.

Function Documentation

density() [1/12]

template<typename BGf, int R>
requires (is_block_gf_v<BGf>)

auto triqs::gfs::density	(	BGf const &	gin,
		std::vector< array< dcomplex, R > > const &	known_moments )

#include <triqs/gfs/functions/density.hpp>

Compute the density block-wise from a block Green's function on a Matsubara or real-frequency mesh.

The density of each block is evaluated with its own known high-frequency moments.

Template Parameters

BGf	The type of the block Green's function.
R	The rank of the per-block known-moment arrays.

Parameters

gin	The block Green's function.
known_moments	Array of known high-frequency moments.

Returns

A vector of per-block densities (matrix or scalar depending on the target shape of each block).

Definition at line 203 of file density.hpp.

density() [2/12]

nda::matrix< dcomplex > triqs::gfs::density	(	gf_const_view< mesh::imfreq >	g,
		array_const_view< dcomplex, 3 >	known_moments = {} )

#include <triqs/gfs/functions/density.cpp>

Compute the density from a Green's function.

The density is reconstructed from the imaginary-frequency data using the high-frequency tail moments \( n = 1, 2, 3 \). Known moments may be passed explicitly; if omitted, they are obtained by tail fitting.

Parameters

g	Input Green's function.
known_moments	Array of known high-frequency moments.

Returns

The density matrix.

Definition at line 49 of file density.cpp.

density() [3/12]

dcomplex triqs::gfs::density	(	gf_const_view< mesh::imfreq, scalar_valued >	g,
		array_const_view< dcomplex, 1 >	known_moments = {} )

#include <triqs/gfs/functions/density.cpp>

Compute the density from a Green's function.

The density is reconstructed from the imaginary-frequency data using the high-frequency tail moments \( n = 1, 2, 3 \). Known moments may be passed explicitly; if omitted, they are obtained by tail fitting.

Parameters

g	Input Green's function.
known_moments	Array of known high-frequency moments.

Returns

The scalar density.

Definition at line 140 of file density.cpp.

density() [4/12]

nda::matrix< dcomplex > triqs::gfs::density

(

gf_const_view< mesh::legendre >

g

)

#include <triqs/gfs/functions/density.cpp>

Compute the density from a Green's function.

The density is obtained directly from the Legendre coefficients.

Parameters

g	Input Green's function.

Returns

The density matrix.

Definition at line 213 of file density.cpp.

density() [5/12]

dcomplex triqs::gfs::density

(

gf_const_view< mesh::legendre, scalar_valued >

g

)

#include <triqs/gfs/functions/density.cpp>

Compute the density from a Green's function.

The density is obtained directly from the Legendre coefficients.

Parameters

g	Input Green's function.

Returns

The scalar density.

Definition at line 225 of file density.cpp.

density() [6/12]

nda::matrix< dcomplex > triqs::gfs::density

(

gf_const_view< mesh::refreq >

g

)

#include <triqs/gfs/functions/density.cpp>

Zero temperature density from integration on the real frequency axis.

Compute the zero-temperature density from a real-frequency Green's function.

Obtained by integrating the spectral function over the negative real axis ( \( T = 0 \) Fermi function).

Parameters

g	Input Green's function.

Returns

The density matrix.

Definition at line 152 of file density.cpp.

density() [7/12]

nda::matrix< dcomplex > triqs::gfs::density	(	gf_const_view< mesh::refreq >	g,
		double	beta )

#include <triqs/gfs/functions/density.cpp>

Finite temperature density from integration on the real frequency axis.

Compute the density from a Green's function.

Obtained by integrating the spectral function weighted by the Fermi function at temperature \( T = 1/\beta \).

Parameters

g	Input Green's function.
beta	Inverse temperature.

Returns

The density matrix.

Definition at line 184 of file density.cpp.

density() [8/12]

dcomplex triqs::gfs::density

(

gf_const_view< mesh::refreq, scalar_valued >

g

)

#include <triqs/gfs/functions/density.cpp>

Compute the zero-temperature density from a real-frequency Green's function.

Obtained by integrating the spectral function over the negative real axis ( \( T = 0 \) Fermi function).

Parameters

g	Input Green's function.

Returns

The scalar density.

Definition at line 207 of file density.cpp.

density() [9/12]

dcomplex triqs::gfs::density	(	gf_const_view< mesh::refreq, scalar_valued >	g,
		double	beta )

#include <triqs/gfs/functions/density.cpp>

Compute the density from a Green's function.

Obtained by integrating the spectral function weighted by the Fermi function at temperature \( T = 1/\beta \).

Parameters

g	Input Green's function.
beta	Inverse temperature.

Returns

The scalar density.

Definition at line 203 of file density.cpp.

density() [10/12]

auto triqs::gfs::density

(

MemoryGf< mesh::dlr > auto const &

g

)

#include <triqs/gfs/functions/density.hpp>

Compute the density from a Green's function.

Parameters

g	Input Green's function.

Returns

The density (matrix).

Definition at line 111 of file density.hpp.

density() [11/12]

auto triqs::gfs::density

(

MemoryGf< mesh::dlr_imfreq > auto const &

g

)

#include <triqs/gfs/functions/density.hpp>

Compute the density from a Green's function.

Parameters

g	Input Green's function.

Returns

The density (matrix).

Definition at line 135 of file density.hpp.

density() [12/12]

auto triqs::gfs::density

(

MemoryGf< mesh::dlr_imtime > auto const &

g

)

#include <triqs/gfs/functions/density.hpp>

Compute the density from a Green's function.

Parameters

g	Input Green's function.

Returns

The density (matrix).

Definition at line 127 of file density.hpp.