#include <triqs_modest/embedding.hpp>

Detailed Description

The embedding class.

The embedding class encodes the mapping between impurities and the correlated space \( \mathcal{C} \) (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)
	Construct an embedding object.

template<typename Mesh >
std::vector< std::pair< block_gf< Mesh, matrix_valued >, block_matrix_t > >	make_zero_imp_self_energies (Mesh const &mesh)
	Zero initialize impurity self-energies.

Accessors
imp_block_t	operator[] (long alpha, long sigma) const
	Bracket accessor: \( \psi[\alpha,\sigma] \).

nda::array< imp_block_t, 2 >	get_psi () const
	The mapping table \( \psi \).

long	n_alpha () const
	Number of blocks in \( \alpha \) for the \( \Sigma_{\text{embed}} \).

long	n_sigma () const
	Number of blocks in \( \sigma \) for the \( \Sigma_{\text{embed}} \).

long	n_gamma (long imp_idx) const
	Number of blocks in \( \gamma \) for the \( \Sigma_{\text{imp}} \) [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 \( \Sigma_{\text{embed}} \).

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 \( \psi \).

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

embedding	flip_spin (long alpha) const
	Flip the spins ( \( \sigma \)) for block \( \alpha \).

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

embedding	split (long imp_idx, std::function< bool(long)> p) const
	Split impurity `imp_idx`.

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 (TRIQS/ModEST).

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 (TRIQS/ModEST).

block2_matrix_t	embed (std::vector< block_matrix_t > const &Sigma_imp_static_vec) const
	Embed block matrices (TRIQS/ModEST).

template<typename Mesh >
std::vector< block_gf< Mesh, matrix_valued > >	extract (block2_gf< Mesh, matrix_valued > const &g_loc) const
	Extract single-particle quantities (TRIQS/ModEST).

std::vector< block_matrix_t >	extract (block2_matrix_t const &matrix_C) const
	Extract matrices (TRIQS/ModEST).

CoQui Ops
Embedding methods which operate on a given object X where X ∈ (nda::array<dcomplex, 4>, nda::array<dcomplex, 5>, etc.) These methods are used to extract and embed quantities in the CoQui format.
std::vector< nda::array< dcomplex, 3 > >	embed_1p (std::vector< std::vector< nda::array< dcomplex, 3 > > > const &Sigma_imp_vec) const
	Embed single-particle quantities (CoQui).

nda::array< dcomplex, 5 >	embed_2p (std::vector< nda::array< dcomplex, 5 > > const &pi_imp_vec) const
	Embed two-particle quantities (CoQui).

nda::array< dcomplex, 4 >	embed_tensor (std::vector< nda::array< dcomplex, 4 > > const &U_tensor_vec) const
	Embed tensors (CoQui).

std::vector< std::vector< nda::array< dcomplex, 3 > > >	extract_1p (nda::array< dcomplex, 4 > const &g_loc) const
	Extract single-particle quantities (CoQui).

std::vector< nda::array< dcomplex, 5 > >	extract_2p (nda::array< dcomplex, 5 > const &Pi_loc) const
	Extract two-particle quantities (CoQui).

std::vector< nda::array< dcomplex, 4 > >	extract_tensor (nda::array< dcomplex, 4 > const &U_tensor) const
	Extract tensors (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)

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
	)

Construct an embedding object.

Parameters

sigma_embed_decomposition	Decomposition (list of block sizes) for \( \Sigma_{\text{embed}} \): \([ \alpha ] = \) block size. Note that the decompositions are given for \( \alpha \), \( \gamma \) index, and are independent of \( \sigma \).
imp_decompositions	List of decomposition of solvers: [n_imp][ \( \gamma \)] = block size.
psi	The mapping \( \psi[\alpha,\sigma]\) -> n_imp, \( \gamma \), \( \tau \).
sigma_names	Names for the values of the \( \sigma \) index (e.g., "up", "down").

Definition at line 18 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 132 of file embedding.cpp.

◆ drop()

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

Remove an impurity from the embedding table \( \psi \).

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

Parameters

imp_idx Index of the impurity to remove from the table \( \psi \).

Returns: New embedding with the updated \( \psi \) map.

Definition at line 235 of file embedding.cpp.

◆ embed() [1/3]

template<typename Mesh >

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

inline

Embed single-particle quantities (TRIQS/ModEST).

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

\( \Sigma_{\text{embed}}^{ασ} = \Sigma_{\text{imp}}^{ψ(α,σ)} \),
\( \psi(\alpha,\sigma) \to \) (n_imp, \( \gamma \), \( \tau \)).

Parameters

Sigma_imp_vec A list of impurity self-energies.

Returns: \( \Sigma_{\text{embed}}[\alpha, \sigma] \) in \( \mathcal{C} \) space using the embed decomposition.

Definition at line 265 of file embedding.hpp.

◆ embed() [2/3]

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

inline

Embed single-particle quantities (TRIQS/ModEST).

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 \( \mathcal{C} \) space as a pair (dynamic, static).

Definition at line 292 of file embedding.hpp.

◆ embed() [3/3]

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

Embed block matrices (TRIQS/ModEST).

Definition at line 307 of file embedding.cpp.

◆ embed_1p()

std::vector< nda::array< dcomplex, 3 > > triqs::modest::embedding::embed_1p ( std::vector< std::vector< nda::array< dcomplex, 3 > > > const & Sigma_imp_vec ) const

Embed single-particle quantities (CoQui).

Definition at line 407 of file embedding.cpp.

◆ embed_2p()

nda::array< dcomplex, 5 > triqs::modest::embedding::embed_2p ( std::vector< nda::array< dcomplex, 5 > > const & pi_imp_vec ) const

Embed two-particle quantities (CoQui).

Definition at line 450 of file embedding.cpp.

◆ embed_tensor()

nda::array< dcomplex, 4 > triqs::modest::embedding::embed_tensor ( std::vector< nda::array< dcomplex, 4 > > const & U_tensor_vec ) const

Embed tensors (CoQui).

Definition at line 363 of file embedding.cpp.

◆ extract() [1/2]

template<typename Mesh >

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

inline

Extract single-particle quantities (TRIQS/ModEST).

Template Parameters

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

Parameters

g_loc Block2Gf of gloc in \( M \times M \) space.

Returns: Local impurity Green's function.

Definition at line 312 of file embedding.hpp.

◆ extract() [2/2]

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

Extract matrices (TRIQS/ModEST).

Definition at line 322 of file embedding.cpp.

◆ extract_1p()

std::vector< std::vector< nda::array< dcomplex, 3 > > > triqs::modest::embedding::extract_1p ( nda::array< dcomplex, 4 > const & g_loc ) const

Extract single-particle quantities (CoQui).

Definition at line 383 of file embedding.cpp.

◆ extract_2p()

std::vector< nda::array< dcomplex, 5 > > triqs::modest::embedding::extract_2p ( nda::array< dcomplex, 5 > const & Pi_loc ) const

Extract two-particle quantities (CoQui).

Definition at line 434 of file embedding.cpp.

◆ extract_tensor()

std::vector< nda::array< dcomplex, 4 > > triqs::modest::embedding::extract_tensor ( nda::array< dcomplex, 4 > const & U_tensor ) const

Extract tensors (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 ( \( \sigma \)) for block \( \alpha \).

For block \( \alpha \) transforms \( (\sigma,\sigma') \to (\tau, \tau') \) to \( (\sigma, \sigma') \to (\tau', \tau)\).

Parameters

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

Returns: New embedding with the updated \( \psi \) map.

Definition at line 218 of file embedding.cpp.

◆ flip_spin() [2/2]

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

Flip the spins ( \( \sigma \)) for all \( [\alpha] \).

For block \( \alpha \) transforms \( (\sigma,\sigma') \to (\tau, \tau') \) to \( (\sigma, \sigma') \to (\tau', \tau)\).

Parameters

alphas A list of alpha blocks to flip the spins.

Returns: New embedding with the updated \( \psi \) map.

Definition at line 227 of file embedding.cpp.

◆ get_psi()

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

inline

The mapping table \( \psi \).

Definition at line 111 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 206 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 129 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

Zero initialize impurity self-energies.

Definition at line 223 of file embedding.hpp.

◆ n_alpha()

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

inline

Number of blocks in \( \alpha \) for the \( \Sigma_{\text{embed}} \).

Definition at line 114 of file embedding.hpp.

◆ n_gamma()

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

inline

Number of blocks in \( \gamma \) for the \( \Sigma_{\text{imp}} \) [imp_idx].

Definition at line 120 of file embedding.hpp.

◆ n_impurities()

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

inline

Number of impurities.

Definition at line 123 of file embedding.hpp.

◆ n_sigma()

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

inline

Number of blocks in \( \sigma \) for the \( \Sigma_{\text{embed}} \).

Definition at line 117 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: \( \psi[\alpha,\sigma] \).

Returns: The corresponding impurity block (n_imp, \( \gamma \), \( \tau \)).

Definition at line 107 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 \( \psi \).

Replaces the impurity solver corresponding to imp_idx_to_remove with the impurity solver at imp_idx_to_replace_with and updates the underlying table \( \psi \).

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_remove`.

Returns: A new embedding with the updated \( \psi \) map.

Definition at line 249 of file embedding.cpp.

◆ sigma_embed_block_shape()

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

Gf block structure for \( \Sigma_{\text{embed}} \).

Definition at line 198 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 126 of file embedding.hpp.

◆ split() [1/3]

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

Split impurity imp_idx.

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

Definition at line 263 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 \( \psi \) map.

Definition at line 298 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

Definition at line 191 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() [1/3]

◆ embed() [2/3]

◆ embed() [3/3]

◆ embed_1p()

◆ embed_2p()

◆ embed_tensor()

◆ extract() [1/2]

◆ extract() [2/2]

◆ extract_1p()

◆ extract_2p()

◆ extract_tensor()

◆ 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<<