One-body elements

Detailed Description

The one-body elements abstraction in ModEST.

Classes
struct	triqs::modest::band_dispersion
	The one-body dispersion as a function of momentum. More...
struct	triqs::modest::downfolding_projector
	The projector that downfolds the energy bands onto a set of localized atomic-like orbitals. More...
struct	triqs::modest::ibz_symmetry_ops
	Irreducible Brillouin Zone (IBZ) symmetry operations to symmetrize observables over the entire Brillouin zone. More...
class	triqs::modest::local_space
	Describe the atomic orbitals within downfolded \(\mathcal{C}\) space. More...
struct	triqs::modest::one_body_elements_on_grid
	A one-body elements struct where all of the underlying data exists on a fixed momentum grid. More...
struct	triqs::modest::one_body_elements_tb
	A one-body elements using a tight-binding Hamiltonian. More...

OBE factories using a fixed grid
Factory functions to create one_body_elements_on_grid
std::pair< double, one_body_elements_on_grid >	triqs::modest::one_body_elements_from_dft_converter (std::string const &filename, double threshold=1.e-5, bool diagonalize_hloc=false)
	Create a one-body elements with orthonormalized projectors.
one_body_elements_on_grid	triqs::modest::one_body_elements_with_theta_projectors (std::string const &filename, one_body_elements_on_grid const &obe)
	Create a one-body elements with the \( \Theta \) projectors.
one_body_elements_on_grid	triqs::modest::one_body_elements_on_high_symmetry_path (std::string const &filename, one_body_elements_on_grid const &obe)
	Create a one-body elements along specific k-path.

OBE factories using a TB Hamiltonian
Factory functions to create one_body_elements_on_tb
one_body_elements_tb	triqs::modest::one_body_elements_from_wannier90 (std::string const &wannier_file_path, spin_kind_e spin_kind, std::vector< atomic_orbs > atomic_shells)
	Construct a one-body elements TB object from Wannier90 in the case of a single spin index.
one_body_elements_tb	triqs::modest::one_body_elements_from_wannier90 (std::string const &wannier_file_path_up, std::string const &wannier_file_path_dn, spin_kind_e spin_kind, std::vector< atomic_orbs > atomic_shells)
	Construct a one-body elements TB object from Wannier90 in the case with separate spin up/spin down channels.

Function Documentation

one_body_elements_from_dft_converter()

std::pair< double, one_body_elements_on_grid > triqs::modest::one_body_elements_from_dft_converter	(	std::string const &	filename,
		double	threshold = 1.e-5,
		bool	diagonalize_hloc = false
	)

#include <triqs_modest/loaders.cpp>

Create a one-body elements with orthonormalized projectors.

Using the data from the "dft_input" group, the band dispersion, local space, downfolding projector, and optional IBZ symmetry ops are prepared to create a one-body elements. This object is intended to be used in DMFT calculations.

Our strategy is to decompose the \({\cal C}\) space using the suitable basis for embedding. Each block of embedded self-energy will then be mapped to corresponding impurity models self-energy.

The projectors are obtained from the DFT code or Wannier90, in some global coordinate system of the crystal. Some basis transformations are required before performing the embedding.

1. A coordinate system rotation \(R^{a}_{m_{a},m_{a}'}\) from the global coordinate system of atom (site) \(a\) into the local coordinate system of the crystal. This rotations ensure that equivalent atoms have the same self-energy in the new basis, hence can be solved by the same impurity model.
2. Optionally, we perform a second rotation \( U \) to infer the irreps from the local Hamiltonian. Unfortunately, at this stage, the proper information about irreps is not retrieved from the electronic structure code. A workaround has been to examine the local non-interacting Hamiltonian:

   \[ [H_{\mathrm{loc}}^{0}]_{m_{a} m_{a}'}^{a,\sigma} \equiv \sum_{\mathbf{k}} P_{(a,m_{a})\nu}^{\sigma} (\mathbf{k}) \varepsilon_{\nu\nu'}^{\sigma}(\mathbf{k}) [P_{(a',m_{\alpha}')\nu'}^{\sigma} (\mathbf{k})]^{\dagger}. \]

Its block structure is infered (up to a user-defined threshold), by discovering a permutation of the orbitals \(m_{a}\) which renders \(H_{\mathrm{loc}}^{0}\) block-diagonal. Optionally, we can diagonalize these smaller blocks of the local non-interacting Hamiltonian (to reduce the off-diagonal elements in the impurity model hybridization functions \(\Delta_{mm'}^{\sigma}\)).

The Wannier basis is therefore transformed as:

\[ P^{\sigma}_{m\nu}(\mathbf{k}) \leftarrow (RU)^{\dagger}_{m, m'} P^{\sigma}_{m'\nu}(\mathbf{k}). \]

Parameters

filename	Hdf5 file from dft_tools converter.
threshold	Off-diagonal threshold for discovery of symmetries.
diagonalize_hloc	Diagonalize the local non-interacting hamiltonian.

Returns

The total electron density and a one-body elements.

Definition at line 253 of file loaders.cpp.

one_body_elements_from_wannier90() [1/2]

one_body_elements_tb triqs::modest::one_body_elements_from_wannier90	(	std::string const &	wannier_file_path,
		spin_kind_e	spin_kind,
		std::vector< atomic_orbs >	atomic_shells
	)

#include <triqs_modest/obe_tb.cpp>

Construct a one-body elements TB object from Wannier90 in the case of a single spin index.

Parameters

wannier_file_path	String to Wannier90 files, including the prefix, as in "path/to/file/seedname" to specify a Wannier files named in the format "seedname_tb.dat".
spin_kind	Spin kind for this calculation.
atomic_shells	List of atomic shells input by the user.

Returns

One-body elements containing the Wannier90 tight binding Hamiltonian.

Definition at line 23 of file obe_tb.cpp.

one_body_elements_from_wannier90() [2/2]

one_body_elements_tb triqs::modest::one_body_elements_from_wannier90	(	std::string const &	wannier_file_path_up,
		std::string const &	wannier_file_path_dn,
		spin_kind_e	spin_kind,
		std::vector< atomic_orbs >	atomic_shells
	)

#include <triqs_modest/obe_tb.cpp>

Construct a one-body elements TB object from Wannier90 in the case with separate spin up/spin down channels.

Parameters

wannier_file_path_up	String to Wannier90 files, including the prefix, for the up spin channel, as in "path/to/file/seedname" to specify a Wannier files named in the format "seedname_tb.dat".
wannier_file_path_dn	String to Wannier90 files, including the prefix, for the down spin channel as in "path/to/file/seedname" to specify a Wannier files named in the format "seedname_tb.dat"
spin_kind	Spin kind for this calculation.
atomic_shells	List of atomic shells input by the user.

Returns

One-body elements containing the Wannier90 tight binding Hamiltonian.

Definition at line 39 of file obe_tb.cpp.

one_body_elements_on_high_symmetry_path()

one_body_elements_on_grid triqs::modest::one_body_elements_on_high_symmetry_path	(	std::string const &	filename,
		one_body_elements_on_grid const &	obe
	)

#include <triqs_modest/loaders.cpp>

Create a one-body elements along specific k-path.

Using the data from the "dft_bands_input" group, the band disperion and downfolding projector are prepared to create one-body elements. This object is intended to be used for post-processing the momentum-resolved spectral function.

Parameters

filename	Hdf5 file from the DFTtools converter.
obe	One-body elements that was ued in the DMFT calculation.

Returns

One-body elements along high-symmetry k-path.

Definition at line 361 of file loaders.cpp.

one_body_elements_with_theta_projectors()

one_body_elements_on_grid triqs::modest::one_body_elements_with_theta_projectors	(	std::string const &	filename,
		one_body_elements_on_grid const &	obe
	)

#include <triqs_modest/loaders.cpp>

Create a one-body elements with the \( \Theta \) projectors.

Using the data from the "dft_parproj_input" group, the local space, downfolding projectors, and optional IBZ symmetry ops are prepared to create a one-body elements. This object is intended to be used for post-processing the atom- and orbitally-resolved k-summed spectral functions.

Parameters

filename	Hdf5 file from DFTtools converter with "dft_parproj_input" group.
obe	One-body elements that was used in the DMFT calculation.

Returns

One-body elements using the \( \Theta \) projectors.

Definition at line 328 of file loaders.cpp.