standardized hdf5 structure

All the DFT input data is stored using the hdf5 standard, as described also in the documentation of the TRIQS package itself. In order to do a DMFT calculation, using input from DFT applications, a converter is needed on order to provide the necessary data in the hdf5 format.

groups and their formats

In order to be used with the DMFT routines, the following data needs to be provided in the hdf5 file. It contains a lot of information in order to perform DMFT calculations for all kinds of situations, e.g. d-p Hamiltonians, more than one correlated atomic shell, or using symmetry operations for the k-summation. We store all data in subgroups of the hdf5 archive:

Main data

There needs to be one subgroup for the main data of the calculation. The default name of this group is dft_input. Its contents are

Name	Type	Meaning
energy_unit	float	Unit of energy used for the calculation.
dft_code	string	DFT code used to generate input data.
n_k	int	Number of k-points used for the BZ integration.
k_dep_projection	int	1 if the dimension of the projection operators depend on the k-point, 0 otherwise.
SP	int	1 for spin-polarised Hamiltonian, 0 for paramagnetic Hamiltonian.
SO	int	1 if spin-orbit interaction is included, 0 otherwise.
charge_below	float	Number of electrons in the crystal below the correlated orbitals. Note that this is for compatibility with dmftproj, otherwise set to 0
density_required	float	Required total electron density. Needed to determine the chemical potential. The density in the projection window is then density_required-charge_below.
symm_op	int	1 if symmetry operations are used for the BZ sums, 0 if all k-points are directly included in the input.
n_shells	int	Number of atomic shells for which post-processing is possible. Note: this is not the number of correlated orbitals! If there are two equivalent atoms in the unit cell, n_shells is 2.
shells	list of dict {string:int}, dim n_shells x 4	Atomic shell information. For each shell, have a dict with keys [‘atom’, ‘sort’, ‘l’, ‘dim’]. ‘atom’ is the atom index, ‘sort’ defines the equivalency of the atoms, ‘l’ is the angular quantum number, ‘dim’ is the dimension of the atomic shell. e.g. for two equivalent atoms in the unit cell, atom runs from 0 to 1, but sort can take only one value 0.
n_corr_shells	int	Number of correlated atomic shells. If there are two correlated equivalent atoms in the unit cell, n_corr_shells is 2.
n_inequiv_shells	int	Number of inequivalent atomic shells. Needs to be smaller than n_corr_shells. The up / downfolding routines mediate between all correlated shells and the actual inequivalent shells, by using the self-energy etc. for all equal shells belonging to the same class of inequivalent shells. The mapping is performed with information stored in corr_to_inequiv and inequiv_to_corr.
corr_to_inequiv	list of int, dim n_corr_shells	mapping from correlated shells to inequivalent correlated shells. A list of length n_corr_shells containing integers, where same numbers mark equivalent sites.
inequiv_to_corr	list of int, dim n_inequiv_shells	A list of length n_inequiv_shells containing list indices as integers pointing to the corresponding sites in corr_to_inequiv.
corr_shells	list of dict {string:int}, dim n_corr_shells x 6	Correlated orbital information. For each correlated shell, have a dict with keys [‘atom’, ‘sort’, ‘l’, ‘dim’, ‘SO’, ‘irrep’]. ‘atom’ is the atom index, ‘sort’ defines the equivalency of the atoms, ‘l’ is the angular quantum number, ‘dim’ is the dimension of the atomic shell. ‘SO’ is one if spin-orbit is included, 0 otherwise, ‘irep’ is a dummy integer 0.
use_rotations	int	1 if local and global coordinate systems are used, 0 otherwise.
rot_mat	list of numpy.array.complex, dim n_corr_shells x [corr_shells[‘dim’],corr_shells[‘dim’]]	Rotation matrices for correlated shells, if use_rotations. These rotations are automatically applied for up / downfolding. Set to the unity matrix if no rotations are used.
rot_mat_time_inv	list of int, dim n_corr_shells	If SP is 1, 1 if the coordinate transformation contains inversion, 0 otherwise. If use_rotations or SP is 0, give a list of zeros.
n_reps	int	Number of irreducible representations of the correlated shell. e.g. 2 if eg/t2g splitting is used.
dim_reps	list of int, dim n_reps	Dimension of the representations. e.g. [2,3] for eg/t2g subsets.
T	list of numpy.array.complex, dim n_inequiv_corr_shell x [max(corr_shell[‘dim’]),max(corr_shell[‘dim’])]	Transformation matrix from the spherical harmonics to impurity problem basis normally the real cubic harmonics). This matrix can be used to calculate the 4-index U matrix, not automatically done.
n_orbitals	numpy.array.int, dim [n_k,SP+1-SO]	Number of Bloch bands included in the projection window for each k-point. If SP+1-SO=2, the number of included bands may depend on the spin projection up/down.
proj_mat	numpy.array.complex, dim [n_k,SP+1-SO,n_corr_shells,max(corr_shell[‘dim’]),max(n_orbitals)]	Projection matrices from Bloch bands to Wannier orbitals. For efficient storage reasons, all matrices must be of the same size (given by last two indices). For k-points with fewer bands, only the first entries are used, the rest are zero. e.g. if number of Bloch bands ranges from 4-6, all matrices are of size 6.
bz_weights	numpy.array.float, dim n_k	Weights of the k-points for the k summation. Soon be replaced by kpt_weights
hopping	numpy.array.complex, dim [n_k,SP+1-SO,max(n_orbitals),max(n_orbitals)]	Non-interacting Hamiltonian matrix for each k point. As for proj_mat, all matrices have to be of the same size.

Converter specific data

This data is specific to the different converters and stored in the dft_input group as well.

For the Vasp converter:

Name	Type	Meaning
kpt_basis	numpy.array.float, dim [3, 3]	Basis for the k-point mesh, reciprocal lattice vectors.
kpts	numpy.array.float, dim [n_k, 3]	k-points given in reciprocal coordinates.
kpt_weights	numpy.array.float, dim [n_k]	Weights of the k-points for the k summation.
proj_or_hk	string	Switch determining whether the Vasp converter is running in projection mode proj, or in Hamiltonian mode hk. In Hamiltonian mode, the hopping matrix is written in orbital basis, whereas in projection mode hopping is written in band basis.
proj_mat_csc	numpy.array.complex, dim [n_k, SP+1-SO, n_corr_shells, max(corr_shell[‘dim’]), max(n_orbitals)]	Projection matrices from Bloch bands to Wannier orbitals for Hamiltonian based hk approach. No site index is given, since hk is written in orbital basis. The last to indices are a square matrix rotating from orbital to band space.
dft_fermi_weights	numpy.array.float, dim [n_k, SP+1-SO, max(n_orbitals)] (stored in dft_misc_input)	DFT fermi weights (occupations) of KS eigenstates for each k-point for calculation of density matrix correction.
band_window	list of numpy.array.int , dim [n_k, 2] (stored in dft_misc_input)	Band windows as KS band indices in Vasp for each spin channel, and k-point. Needed for writing out the GAMMA file.

Symmetry operations

In this subgroup we store all the data for applying the symmetry operations in the DMFT loop (in case you want to use symmetry operations). The default name of this subgroup is dft_symmcorr_input. This information is needed only if symmetry operations are used to do the k summation. To be continued…

Warning

TO BE COMPLETED!

General and simple H(k) Converter

The above described converter of the Wien2k input is quite involved, since Wien2k provides a lot of information, e.g. about symmetry operations, that can be used in the calculation. However, sometimes we want to use a light implementation where the input consists basically only of the Hamiltonian matrix in Wannier basis, given at a grid of k points in the first Brillouin zone. For this purpose, a simple converter is included in the package, called HkConverter, which is implemented for the simplest case of paramagnetic DFT calculations without spin-orbit coupling. It reads a simple, easy to construct text file, and produces an archive that can be used for the DMFT calculations. An example input file for a structure with one correlated site with 3 t2g orbitals in the unit cell contains the following:

10 <- n_k

1.0 <- density_required

1 <- n_shells

1 1 2 3 <- shells, as above: atom, sort, l, dim

1 <- n_corr_shells

1 1 2 3 0 0 <- corr_shells, as above: atom, sort, l, dim, SO, dummy

2 2 3 <- n_reps, dim_reps (length 2, because eg/t2g splitting) for each inequivalent correlated shell

After this header, we give the Hamiltonian matrices for al the k-points. for each k-point we give first the matrix of the real part, then the matrix of the imaginary part. The projection matrices are set automatically to unity matrices, no rotations, no symmetry operations are used. That means that the symmetry sub group in the hdf5 archive needs not be set, since it is not used. It is furthermore assumed that all k-points have equal weight in the k-sum. Note that the input file should contain only the numbers, not the comments given in above example.

The Hamiltonian matrices can be taken, e.g., from Wannier90, which constructs the Hamiltonian in a maximally localized Wannier basis.

Note that with this simplified converter, no full charge self consistent calculations are possible!