#include <triqs_modest/embedding.hpp>

Detailed Description

The embedding class.

The embeddding class encodes the mapping between impurities and the correlated space 𝓒 (cf. ModEST implementation notes). In particular, it maps the individual "blocks" within an impurity self-energy to a block and spin of the embedded self-energy function, which can then be upfolded (downfolded) to obtain the lattice self-energy and the local Green's function.

Definition at line 29 of file embedding.hpp.

Public Member Functions
	embedding (std::vector< long > sigma_embed_decomposition, std::vector< std::vector< long > > imp_decompositions, nda::array< imp_block_t, 2 > psi, std::vector< std::string > sigma_names)
	Default constructor.

template<typename Mesh >
std::vector< std::pair< block_gf< Mesh, matrix_valued >, block_matrix_t > >	make_zero_imp_self_energies (Mesh const &mesh)

Accessors
imp_block_t	operator[] (long alpha, long sigma) const
	bracket accessor: [α, σ] -> the corresponding impurity block (n_imp, γ, τ)

nda::array< imp_block_t, 2 >	get_psi () const
	the mapping table ψ

long	n_alpha () const
	Number of blocks in α for the Σ_embed.

long	n_sigma () const
	Number of blocks in σ for the Σ_embed.

long	n_gamma (long imp_idx) const
	Number of blocks in γ for the Σ_imp[imp_idx].

long	n_impurities () const
	Number of impurities.

std::vector< std::string >	sigma_names () const
	The names of the sigma indices.

std::vector< long >	imp_decomposition (long imp_idx) const
	The impurity decomposition.

C2PY_IGNORE gf_struct2_t	sigma_embed_block_shape () const
	Gf block structure for Σ_embed.

std::vector< gf_struct_t >	imp_block_shape () const
	Gf block structure for the impurity solvers.

std::string	description (bool verbosity=false) const
	Summarize the embedding object.

Unary Ops
Embedding methods which operate on itself and return a new Embedding object.
bool	operator== (embedding const &other) const =default

embedding	drop (long imp_idx) const
	Remove an impurity from the embedding table ψ

embedding	replace (long imp_idx_to_remove, long imp_idx_to_replace_with) const
	Replaces one impurity in the embedding table ψ.

embedding	flip_spin (long alpha) const
	Flip the spins (σ) for block α.

embedding	flip_spin (std::vector< long > alphas) const
	Flip the spins (σ) for all [α].

embedding	split (long imp_idx, std::function< bool(long)> p) const
	Predicate p (long block_idx) -> 0 or 1.

embedding	split (long imp_idx, std::vector< long > const &block_list) const
	Split impurity imp_idx based on block_list.

embedding	split (long imp_idx, std::initializer_list< const char * > x)=delete

Complex Ops
Embedding methods which operate on a given object X where X ∈ (block2gf, block_gf, block_matrix, etc.)
template<typename Mesh >
block2_gf< Mesh, matrix_valued >	embed (std::vector< block_gf< Mesh, matrix_valued > > const &Sigma_imp_vec) const
	embed single-particle quantities

template<typename Mesh >
std::pair< block2_gf< Mesh, matrix_valued >, block2_matrix_t >	embed (std::vector< block_gf< Mesh, matrix_valued > > const &Sigma_imp_vec, std::vector< block_matrix_t > const &Sigma_imp_static_vec) const
	embed single-particle quantities

block2_matrix_t	embed (std::vector< block_matrix_t > const &Sigma_imp_static_vec) const
	embed block matrices

nda::array< nda::array< dcomplex, 3 >, 2 >	embed (std::vector< std::vector< nda::array< dcomplex, 3 > > > const &Sigma_imp_vec) const
	embed single-particle quantities (coqui)

std::vector< nda::array< dcomplex, 5 > >	embed (std::vector< nda::array< dcomplex, 5 > > const &pi_imp_vec) const
	embed two-particle quantities (coqui)

template<typename Mesh >
std::vector< block_gf< Mesh, matrix_valued > >	extract (block2_gf< Mesh, matrix_valued > const &g_loc) const
	embed tensors

std::vector< block_matrix_t >	extract (block2_matrix_t const &matrix_C) const
	extract matrices

std::vector< std::vector< nda::array< dcomplex, 3 > > >	extract (nda::array< dcomplex, 4 > const &g_loc) const
	extract single-particle quantities (CoQui)

std::vector< nda::array< dcomplex, 5 > >	extract (nda::array< dcomplex, 5 > const &Pi_loc) const
	extract two-particle quantities (CoQui)

Friends
void	h5_read (h5::group g, std::string const &name, embedding &x)

void	h5_write (h5::group g, std::string const &name, embedding const &x)
	h5 read/write

std::ostream &	operator<< (std::ostream &out, embedding const &E)
	stream

Constructor & Destructor Documentation

◆ embedding()

triqs::modest::embedding::embedding	(	std::vector< long >	sigma_embed_decomposition,
		std::vector< std::vector< long > >	imp_decompositions,
		nda::array< imp_block_t, 2 >	psi,
		std::vector< std::string >	sigma_names
	)

Default constructor.

Constructor

Parameters

sigma_embed_decomposition Decomposition (list of block sizes) for Σ_embed: [α] = block size

Note: The decompositions are given for α, γ index, and are independent of σ

Parameters

imp_decompositions	List of decomposition of solvers: [n_imp][γ] = block size
psi	The mapping ψ[α,σ] -> n_imp, γ, τ
sigma_names	Names for the values of the σ index (e.g., "up", "down")

Definition at line 16 of file embedding.cpp.

Member Function Documentation

◆ description()

std::string triqs::modest::embedding::description ( bool verbosity = false ) const

Summarize the embedding object.

Definition at line 98 of file embedding.cpp.

◆ drop()

embedding triqs::modest::embedding::drop ( long imp_idx ) const

Remove an impurity from the embedding table ψ

Remove the impurity imp_idx, maps the corresponding α blocks to -1 (i.e. no longer connected to an impurity) and relabel the other impurities with number > imp_idx.

Parameters

imp_idx Index of the impurity to remove from the table ψ

Returns: New embedding with the updated ψ map.

Definition at line 200 of file embedding.cpp.

◆ embed() [1/5]

template<typename Mesh >

block2_gf< Mesh, matrix_valued > triqs::modest::embedding::embed ( std::vector< block_gf< Mesh, matrix_valued > > const & Sigma_imp_vec ) const

embed single-particle quantities

Embed impurity solver self-energies into an embedded self-energy.

\Sigma_{embed}^{ασ} = \Sigma_{imp}^{ψ(α,σ)} ψ(α,σ) -> (n_imp, γ, τ)

Parameters

Sigma_imp_vec a list of impurity self-energies

Returns: Σ_embed[alpha, sigma] in C space using the embed decomposition

Definition at line 315 of file embedding.hpp.

◆ embed() [2/5]

template<typename Mesh >

std::pair< block2_gf< Mesh, matrix_valued >, block2_matrix_t > triqs::modest::embedding::embed	(	std::vector< block_gf< Mesh, matrix_valued > > const &	Sigma_imp_vec,
		std::vector< block_matrix_t > const &	Sigma_imp_static_vec
	)		const

embed single-particle quantities

Embed the impurity self-energy decomposed as a list of dynamic and a list of static parts.

Template Parameters

Mesh	The type of mesh

Parameters

Sigma_imp_vec	A list of dynamic impurity self-energies
Sigma_imp_static_vec	A list of static impurity self-energies

Returns: The self-energy in the C space as a pair (dynamic, static).

Definition at line 340 of file embedding.hpp.

◆ embed() [3/5]

block2_matrix_t triqs::modest::embedding::embed ( std::vector< block_matrix_t > const & Sigma_imp_static_vec ) const

embed block matrices

Definition at line 272 of file embedding.cpp.

◆ embed() [4/5]

std::vector< nda::array< dcomplex, 5 > > triqs::modest::embedding::embed ( std::vector< nda::array< dcomplex, 5 > > const & pi_imp_vec ) const

embed two-particle quantities (coqui)

Definition at line 362 of file embedding.cpp.

◆ embed() [5/5]

nda::array< nda::array< dcomplex, 3 >, 2 > triqs::modest::embedding::embed ( std::vector< std::vector< nda::array< dcomplex, 3 > > > const & Sigma_imp_vec ) const

embed single-particle quantities (coqui)

Definition at line 335 of file embedding.cpp.

◆ extract() [1/4]

template<typename Mesh >

std::vector< block_gf< Mesh, matrix_valued > > triqs::modest::embedding::extract ( block2_gf< Mesh, matrix_valued > const & g ) const

embed tensors

Extract the impurity Green's function.

extract single-particle quantities (ModEST)

Template Parameters

Mesh	The mesh type triqs::mesh::{dlr_imfreq, imfreq}

Parameters

g	Block2Gf of gloc in MxM space

Returns: local impurity Green's function

Definition at line 357 of file embedding.hpp.

◆ extract() [2/4]

std::vector< block_matrix_t > triqs::modest::embedding::extract ( block2_matrix_t const & matrix_C ) const

extract matrices

Definition at line 286 of file embedding.cpp.

◆ extract() [3/4]

std::vector< std::vector< nda::array< dcomplex, 3 > > > triqs::modest::embedding::extract ( nda::array< dcomplex, 4 > const & g_loc ) const

extract single-particle quantities (CoQui)

Definition at line 311 of file embedding.cpp.

◆ extract() [4/4]

std::vector< nda::array< dcomplex, 5 > > triqs::modest::embedding::extract ( nda::array< dcomplex, 5 > const & Pi_loc ) const

extract two-particle quantities (CoQui)

Definition at line 346 of file embedding.cpp.

◆ flip_spin() [1/2]

embedding triqs::modest::embedding::flip_spin ( long alpha ) const

Flip the spins (σ) for block α.

For block α transforms (σ,σ') -> (τ, τ') to (σ, σ') -> (τ', τ).

Parameters

alpha the index of the alpha block to flip the spins.

Returns: a new embedding with the updated ψ map.

Definition at line 184 of file embedding.cpp.

◆ flip_spin() [2/2]

embedding triqs::modest::embedding::flip_spin ( std::vector< long > alphas ) const

Flip the spins (σ) for all [α].

For block α transforms (σ,σ') -> (τ, τ') to (σ, σ') -> (τ', τ).

Parameters

alphas a list of alpha blocks to flip the spins.

Returns: New embedding with the updated ψ map.

Definition at line 192 of file embedding.cpp.

◆ get_psi()

nda::array< imp_block_t, 2 > triqs::modest::embedding::get_psi ( ) const

inline

the mapping table ψ

Definition at line 103 of file embedding.hpp.

◆ imp_block_shape()

std::vector< gf_struct_t > triqs::modest::embedding::imp_block_shape ( ) const

Gf block structure for the impurity solvers.

Definition at line 172 of file embedding.cpp.

◆ imp_decomposition()

std::vector< long > triqs::modest::embedding::imp_decomposition ( long imp_idx ) const

inline

The impurity decomposition.

Definition at line 121 of file embedding.hpp.

◆ make_zero_imp_self_energies()

template<typename Mesh >

std::vector< std::pair< block_gf< Mesh, matrix_valued >, block_matrix_t > > triqs::modest::embedding::make_zero_imp_self_energies ( Mesh const & mesh )

inline

Definition at line 206 of file embedding.hpp.

◆ n_alpha()

long triqs::modest::embedding::n_alpha ( ) const

inline

Number of blocks in α for the Σ_embed.

Definition at line 106 of file embedding.hpp.

◆ n_gamma()

long triqs::modest::embedding::n_gamma ( long imp_idx ) const

inline

Number of blocks in γ for the Σ_imp[imp_idx].

Definition at line 112 of file embedding.hpp.

◆ n_impurities()

long triqs::modest::embedding::n_impurities ( ) const

inline

Number of impurities.

Definition at line 115 of file embedding.hpp.

◆ n_sigma()

long triqs::modest::embedding::n_sigma ( ) const

inline

Number of blocks in σ for the Σ_embed.

Definition at line 109 of file embedding.hpp.

◆ operator==()

bool triqs::modest::embedding::operator== ( embedding const & other ) const

default

◆ operator[]()

imp_block_t triqs::modest::embedding::operator[]	(	long	alpha,
		long	sigma
	)		const

inline

bracket accessor: [α, σ] -> the corresponding impurity block (n_imp, γ, τ)

Definition at line 99 of file embedding.hpp.

◆ replace()

embedding triqs::modest::embedding::replace	(	long	imp_idx_to_remove,
		long	imp_idx_to_replace_with
	)		const

Replaces one impurity in the embedding table ψ.

Replaces the impurity solver corresponding to imp_idx_to with the impurity solver at imp_idx_from and updates the underlying table ψ.

Parameters

imp_idx_to_remove	the index of the impurity solver to be replaced.
imp_idx_to_replace_with	the index of the impurity solver that will replace imp_idx_to.

Returns: a new embedding with the updated ψ map.

Definition at line 214 of file embedding.cpp.

◆ sigma_embed_block_shape()

gf_struct2_t triqs::modest::embedding::sigma_embed_block_shape ( ) const

Gf block structure for Σ_embed.

Definition at line 164 of file embedding.cpp.

◆ sigma_names()

std::vector< std::string > triqs::modest::embedding::sigma_names ( ) const

inline

The names of the sigma indices.

Definition at line 118 of file embedding.hpp.

◆ split() [1/3]

embedding triqs::modest::embedding::split	(	long	imp_idx,
		std::function< bool(long)>	p
	)		const

Predicate p (long block_idx) -> 0 or 1.

Definition at line 228 of file embedding.cpp.

◆ split() [2/3]

embedding triqs::modest::embedding::split	(	long	imp_idx,
		std::initializer_list< const char * >	x
	)

delete

◆ split() [3/3]

embedding triqs::modest::embedding::split	(	long	imp_idx,
		std::vector< long > const &	block_list
	)		const

Split impurity imp_idx based on block_list.

For impurity imp_idx, split part of its blocks into a new impurity. The blocks that were split off remain mapped to their original alpha blocks with the updated imp_idx.

Parameters

imp_idx	Impurity number
block_list	A list of blocks of imp_idx to split off.

Returns: New embedding with the updated ψ map.

Definition at line 263 of file embedding.cpp.

Friends And Related Symbol Documentation

◆ h5_read

void h5_read	(	h5::group	g,
		std::string const &	name,
		embedding &	x
	)

friend

Definition at line 96 of file h5.cpp.

◆ h5_write

void h5_write	(	h5::group	g,
		std::string const &	name,
		embedding const &	x
	)

friend

h5 read/write

Definition at line 104 of file h5.cpp.

◆ operator<<

std::ostream & operator<<	(	std::ostream &	out,
		embedding const &	E
	)

friend

stream

Definition at line 157 of file embedding.cpp.

The documentation for this class was generated from the following files:

triqs_modest/embedding.hpp
triqs_modest/embedding.cpp

Detailed Description

Public Member Functions

Friends

Constructor & Destructor Documentation

◆ embedding()

Member Function Documentation

◆ description()

◆ drop()

◆ embed() [1/5]

◆ embed() [2/5]

◆ embed() [3/5]

◆ embed() [4/5]

◆ embed() [5/5]

◆ extract() [1/4]

◆ extract() [2/4]

◆ extract() [3/4]

◆ extract() [4/4]

◆ flip_spin() [1/2]

◆ flip_spin() [2/2]

◆ get_psi()

◆ imp_block_shape()

◆ imp_decomposition()

◆ make_zero_imp_self_energies()

◆ n_alpha()

◆ n_gamma()

◆ n_impurities()

◆ n_sigma()

◆ operator==()

◆ operator[]()

◆ replace()

◆ sigma_embed_block_shape()

◆ sigma_names()

◆ split() [1/3]

◆ split() [2/3]

◆ split() [3/3]

Friends And Related Symbol Documentation

◆ h5_read

◆ h5_write

◆ operator<<