#include <triqs_modest/local_space.hpp>

Detailed Description

Describe the atomic orbitals within downfolded \(\mathcal{C}\) space.

The local space \( \mathcal{C} \) defines the correlated subspace which defines impurities to be solved within DMFT.

The DFT + DMFT equations involve three different spaces, following (mostly) the notations of [S. Beck et al. 2022]:

The (reduced) Bloch space \({\cal B}\) contains bands of dispersion \(\varepsilon_{\nu}^{\sigma}(\mathbf{k})\), in some window of energy. Here, \(\nu\) is the band index ( \(0 \leq \nu < N_\nu^{\mathbf{k}}\)) and \(\mathbf{k}\) is a point in the Brillouin zone. We define \(N_\nu \equiv \mathrm{max}_{\mathbf{k}} N_\nu^{\mathbf{k}}\).
The Wannier space \({\cal W}\) is spanned from Wannier functions constructed from \({\cal B}\).
The correlated space \({\cal C} \subseteq {\cal W}\) containing \(M\) Wannier orbitals, is a subspace of the Wannier space, in which the self-energy is approximated by the embedding. \({\cal C}\) is spanned by Wannier functions at several atoms/sites with index \(a\) at position \(R_a\) and orbital/Wannier index \(m_{a}\). \({\cal C}\) is indexed by a composite index \(m = (a, m_{a})\), with \(0\leq m \leq M-1\) and \(M=\sum_{a}\mathrm{max}(m_{a}\)). We will write the main equations with the composite \(m\) index, as the \(m = (a, m_{a})\) decomposition of \(m\) is not, in general, appropriate for embeddings.

The \(\sigma\) index is a general block diagonal index. In simple cases, it is the spin index, but not always.

In "spin (non-)polarized" computations, \(\sigma\) is the spin index.
In spin-orbit or Nambu computations, the spin index is merged with \(m\) and \(\nu\), so \(\sigma =0\) (i.e. one value of the index, equivalent to no index at all).

Definition at line 61 of file local_space.hpp.

Public Member Functions
	local_space (spin_kind_e spin_kind, std::vector< atomic_orbs > atomic_shells, nda::array< std::vector< long >, 2 > irreps_decomp_per_atom, nda::array< nda::matrix< dcomplex >, 2 > rotation_from_dft_to_local_basis, nda::array< nda::matrix< dcomplex >, 1 > rotation_from_spherical_to_dft_basis)
	Construct a new local space object.

Accessors
spin_kind_e	spin_kind () const
	Spin kind of \( \sigma \) index.

long	n_sigma () const
	Dimension of the \( \sigma \) index.

std::vector< std::string >	sigma_names () const
	Names of spin indices for naming blocks in block GFs.

long	dim () const
	Dimension of the correlated space.

std::vector< atomic_orbs > const &	atomic_shells () const
	List of all atomic shells spanning the \( \mathcal{C} \) space.

long	n_atoms () const
	The number of atoms.

nda::array< std::vector< long >, 2 > const &	atoms_block_decomposition () const
	2-dim array of all blocks spanning \( \mathcal{C} \) space -> atoms_block_decomposition.

nda::array< nda::matrix< dcomplex >, 2 > const &	rotation_from_dft_to_local_basis () const
	2-dim array of all \( (a, \sigma) \) local rotation matices that rotate the data.

nda::array< nda::matrix< dcomplex >, 1 > const &	rotation_from_spherical_to_dft_basis () const
	Array of rotation matrices from spherical harmonics to dft specific orbital basis.

long	first_shell_of_its_equiv_cls (long idx) const
	Given the index of an atomic shell, return the index of the first atomic shell of its equivalence class.

std::vector< std::string >	atom_names () const
	Names of the atoms in the orbital set.

auto	atomic_decomposition () const
	Transformed view containing the dimension of each atomic shell.

Views and shapes
template<typename Mesh >
block2_gf< Mesh >	atomic_view (block2_gf< Mesh > const &G_C)
	Views a 2-dim block GF according to the atomic decomposition.

nda::array< nda::matrix< dcomplex >, 2 >	atomic_view (nda::array< nda::matrix< dcomplex >, 2 > const &matrix_C)
	Creates an atomic view of block matrices by extracting specific slices based on the atomic decomposition of the current object.

C2PY_IGNORE gf_struct2_t	Gc_block_shape () const
	Shape of the Green function in the correlated space, without block decomposition.

C2PY_IGNORE gf_struct2_t	Gatom_block_shape () const
	Shape of the Green function in the correlated space, decomposed by atomic shells.

Friends
void	h5_read (h5::group g, std::string const &name, local_space &ls)
	h5 read/write

void	h5_write (h5::group g, std::string const &name, local_space const &ls)

Constructor & Destructor Documentation

◆ local_space()

triqs::modest::local_space::local_space	(	spin_kind_e	spin_kind,
		std::vector< atomic_orbs >	atomic_shells,
		nda::array< std::vector< long >, 2 >	irreps_decomp_per_atom,
		nda::array< nda::matrix< dcomplex >, 2 >	rotation_from_dft_to_local_basis,
		nda::array< nda::matrix< dcomplex >, 1 >	rotation_from_spherical_to_dft_basis
	)

Construct a new local space object.

Parameters

spin_kind	Kind of \( \sigma \) index.
atomic_shells	List of all atomic orbitals.
irreps_decomp_per_atom	List of all blocks spanning \( \mathcal{C} \) space -> atoms_block_decomposition.
rotation_from_dft_to_local_basis	Rotation matices from DFT to local basis.
rotation_from_spherical_to_dft_basis	Rotation matrices from spherical to DFT basis.

Definition at line 10 of file local_space.cpp.

Member Function Documentation

◆ atom_names()

std::vector< std::string > triqs::modest::local_space::atom_names ( ) const

inline

Names of the atoms in the orbital set.

Definition at line 148 of file local_space.hpp.

◆ atomic_decomposition()

auto triqs::modest::local_space::atomic_decomposition ( ) const

inline

Transformed view containing the dimension of each atomic shell.

Definition at line 151 of file local_space.hpp.

◆ atomic_shells()

std::vector< atomic_orbs > const & triqs::modest::local_space::atomic_shells ( ) const

inline

List of all atomic shells spanning the \( \mathcal{C} \) space.

Definition at line 127 of file local_space.hpp.

◆ atomic_view() [1/2]

template<typename Mesh >

block2_gf< Mesh > triqs::modest::local_space::atomic_view ( block2_gf< Mesh > const & G_C )

inline

Views a 2-dim block GF according to the atomic decomposition.

Template Parameters

Mesh	The Green's function meesh

Parameters

G_C	A 2-dim block GF spanning the entire \( \mathcal{C} \) space [0, sigma](M, M).

Returns: A 2-dim block GF in the atomic decomposition view [atom, sigma][m_orb, m_orb].

Definition at line 170 of file local_space.hpp.

◆ atomic_view() [2/2]

nda::array< nda::matrix< dcomplex >, 2 > triqs::modest::local_space::atomic_view ( nda::array< nda::matrix< dcomplex >, 2 > const & matrix_C )

Creates an atomic view of block matrices by extracting specific slices based on the atomic decomposition of the current object.

Parameters

matrix_C The input block matrices object from which the atomic view is created.

Returns: 2-dim array containing the new block matrices in the atomic view.

Definition at line 34 of file local_space.cpp.

◆ atoms_block_decomposition()

nda::array< std::vector< long >, 2 > const & triqs::modest::local_space::atoms_block_decomposition ( ) const

inline

2-dim array of all blocks spanning \( \mathcal{C} \) space -> atoms_block_decomposition.

Definition at line 134 of file local_space.hpp.

◆ dim()

long triqs::modest::local_space::dim ( ) const

inline

Dimension of the correlated space.

Definition at line 124 of file local_space.hpp.

◆ first_shell_of_its_equiv_cls()

long triqs::modest::local_space::first_shell_of_its_equiv_cls ( long idx ) const

Given the index of an atomic shell, return the index of the first atomic shell of its equivalence class.

Definition at line 26 of file local_space.cpp.

◆ Gatom_block_shape()

C2PY_IGNORE gf_struct2_t triqs::modest::local_space::Gatom_block_shape ( ) const

inline

Shape of the Green function in the correlated space, decomposed by atomic shells.

Definition at line 197 of file local_space.hpp.

◆ Gc_block_shape()

gfs::gf_struct2_t triqs::modest::local_space::Gc_block_shape ( ) const

Shape of the Green function in the correlated space, without block decomposition.

Definition at line 44 of file local_space.cpp.

◆ n_atoms()

long triqs::modest::local_space::n_atoms ( ) const

inline

The number of atoms.

Definition at line 130 of file local_space.hpp.

◆ n_sigma()

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

inline

Dimension of the \( \sigma \) index.

Definition at line 115 of file local_space.hpp.

◆ rotation_from_dft_to_local_basis()

nda::array< nda::matrix< dcomplex >, 2 > const & triqs::modest::local_space::rotation_from_dft_to_local_basis ( ) const

inline

2-dim array of all \( (a, \sigma) \) local rotation matices that rotate the data.

Definition at line 137 of file local_space.hpp.

◆ rotation_from_spherical_to_dft_basis()

nda::array< nda::matrix< dcomplex >, 1 > const & triqs::modest::local_space::rotation_from_spherical_to_dft_basis ( ) const

inline

Array of rotation matrices from spherical harmonics to dft specific orbital basis.

Definition at line 140 of file local_space.hpp.

◆ sigma_names()

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

inline

Names of spin indices for naming blocks in block GFs.

Definition at line 118 of file local_space.hpp.

◆ spin_kind()

spin_kind_e triqs::modest::local_space::spin_kind ( ) const

inline

Spin kind of \( \sigma \) index.

Definition at line 112 of file local_space.hpp.

Friends And Related Symbol Documentation

◆ h5_read

void h5_read	(	h5::group	g,
		std::string const &	name,
		local_space &	ls
	)

friend

h5 read/write

Definition at line 81 of file h5.cpp.

◆ h5_write

void h5_write	(	h5::group	g,
		std::string const &	name,
		local_space const &	ls
	)

friend

Definition at line 88 of file h5.cpp.

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

triqs_modest/local_space.hpp
triqs_modest/local_space.cpp

Detailed Description

Public Member Functions

Friends

Constructor & Destructor Documentation

◆ local_space()

Member Function Documentation

◆ atom_names()

◆ atomic_decomposition()

◆ atomic_shells()

◆ atomic_view() [1/2]

◆ atomic_view() [2/2]

◆ atoms_block_decomposition()

◆ dim()

◆ first_shell_of_its_equiv_cls()

◆ Gatom_block_shape()

◆ Gc_block_shape()

◆ n_atoms()

◆ n_sigma()

◆ rotation_from_dft_to_local_basis()

◆ rotation_from_spherical_to_dft_basis()

◆ sigma_names()

◆ spin_kind()

Friends And Related Symbol Documentation

◆ h5_read

◆ h5_write