Class for diagonalizing electronic energies with the Wannier interpolation The object is built passing the information produced by the file _tb.dat of Wannier90, and can be used to compute the interpolated band structure.

#include <electron_h0_wannier.h>

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Public Member Functions
	ElectronH0Wannier (const Eigen::Matrix3d &directUnitCell_, const Eigen::MatrixXd &bravaisVectors_, const Eigen::VectorXd &vectorsDegeneracies_, const Eigen::Tensor< std::complex< double >, 3 > &h0R_, const Eigen::Tensor< std::complex< double >, 4 > *rMatrix_=nullptr)
	Constructor for the electronic Hamiltonian in the Wannier case. More...

	ElectronH0Wannier (const ElectronH0Wannier &that)
	Copy constructor.

ElectronH0Wannier &	operator= (const ElectronH0Wannier &that)
	Copy assignment.

	~ElectronH0Wannier ()
	Class destructor.

Particle	getParticle () override
	Method to return that the underlying is that of an electronic Fermion.

int	getNumBands () override
	get the total number of bands. More...

std::tuple< Eigen::VectorXd, Eigen::MatrixXcd >	diagonalize (Point &point) override
	get the electronic energies (in Ry) at a single k-point. More...

std::tuple< Eigen::VectorXd, Eigen::MatrixXcd >	diagonalizeFromCoordinates (Eigen::Vector3d &k) override
	Diagonalize the Harmonic Hamiltonian at an arbitrary wavevector. More...

std::tuple< std::vector< Eigen::VectorXd >, std::vector< Eigen::MatrixXcd > >	batchedDiagonalizeFromCoordinates (std::vector< Eigen::Vector3d > &cartesianWavevectors)
	Computes energies and eigenvectors of electrons for a batch of nk wavevectors. More...

std::vector< Eigen::MatrixXcd >	batchedBuildHamiltonians (std::vector< Eigen::Vector3d > &cartesianWavevectors)
	Computes the Fourier transform of the Wannier Hamiltonian at a batch of wavevectors. More...

StridedComplexView3D	kokkosBatchedBuildBlochHamiltonian (const DoubleView2D &cartesianCoordinates) override
	Computes the Fourier transform of the Wannier Hamiltonian at a batch of wavevectors. More...

std::tuple< DoubleView2D, StridedComplexView3D >	kokkosBatchedDiagonalizeFromCoordinates (const DoubleView2D &cartesianCoordinates, const bool withMassScaling=true) override
	Computes energies and eigenvectors of electrons for a batch of nk wavevectors. More...

std::tuple< DoubleView2D, StridedComplexView3D, ComplexView4D >	kokkosBatchedDiagonalizeWithVelocities (const DoubleView2D &cartesianCoordinates) override
	Using kokkos, computes the electronic properties of a batch of wavevectors. More...

Eigen::Tensor< std::complex< double >, 3 >	diagonalizeVelocity (Point &point) override
	get the electron velocities (in atomic units) at a single k-point. More...

Eigen::Tensor< std::complex< double >, 3 >	diagonalizeVelocityFromCoordinates (Eigen::Vector3d &coordinates) override

std::tuple< std::vector< Eigen::VectorXd >, std::vector< Eigen::MatrixXcd >, std::vector< Eigen::Tensor< std::complex< double >, 3 > > >	batchedDiagonalizeWithVelocities (std::vector< Eigen::Vector3d > cartesianCoordinates)
	Same as diagonalizeVelocityFromCoordinates, but constructs the velocity operator for a batch of wavevectors. More...

FullBandStructure	populate (Points &fullPoints, const bool &withVelocities, const bool &withEigenvectors, const bool isDistributed=false) override
	This method constructs an electron band structure. More...

std::tuple< std::vector< Eigen::VectorXd >, std::vector< Eigen::MatrixXcd >, std::vector< Eigen::Tensor< std::complex< double >, 3 > > >	populate (const std::vector< Eigen::Vector3d > &cartesianCoordinates, const bool &withVelocities, const bool &withEigenvectors)
	Runs populate on a points list, without creating a new bandstructure object this is necessary if we need energies for some non-uniform grid of points currently this only used by the phonon electron scattering calculation. More...

FullBandStructure	cpuPopulate (Points &fullPoints, const bool &withVelocities, const bool &withEigenvectors, const bool isDistributed=false)
	Internal helper function for cpu diag of electron H0.

std::tuple< std::vector< Eigen::VectorXd >, std::vector< Eigen::MatrixXcd >, std::vector< Eigen::Tensor< std::complex< double >, 3 > > >	kokkosPopulate (const std::vector< Eigen::Vector3d > &cartesianCoordinates, const bool &withVelocities, const bool &withEigenvectors, const std::vector< int > &iks)
	Internal helper function for kokkos diag of electron H0.

std::vector< Eigen::MatrixXcd >	getBerryConnection (Point &point)
	compute the Berry connection <u_mk\| nabla_k \|u_nk> at arb. More...

void	addShiftedVectors (Eigen::Tensor< double, 3 > degeneracyShifts_, Eigen::Tensor< double, 5 > vectorsShifts_)
	Function used during parsing, to add the shifts used in the phases for the Fourier interpolation. More...

int	estimateBatchSize (const bool &withVelocity) override
	Estimate how many k-points we can compute on the GPU in one batch. More...

Public Member Functions inherited from HarmonicHamiltonian
void	kokkosBatchedTreatDegenerateVelocities (const DoubleView2D &cartesianCoordinates, const DoubleView2D &resultEnergies, ComplexView4D &resultVelocities, const double &threshold)

Protected Member Functions
double	getDeviceMemoryUsage ()
	Checks the size of Device-allocated views. More...

Protected Attributes
Particle	particle

Eigen::MatrixXd	bravaisVectors

Eigen::VectorXd	vectorsDegeneracies

Eigen::Matrix3d	directUnitCell

Eigen::Tensor< std::complex< double >, 3 >	h0R

Eigen::Tensor< std::complex< double >, 4 >	rMatrix

int	numWannier

int	numVectors

Eigen::Tensor< double, 3 >	degeneracyShifts

Eigen::Tensor< double, 5 >	vectorsShifts

bool	hasShiftedVectors = false

ComplexView3D	h0R_d

DoubleView3D	degeneracyShifts_d

DoubleView5D	vectorsShifts_d

DoubleView1D	vectorsDegeneracies_d

DoubleView2D	bravaisVectors_d

Constructor & Destructor Documentation

◆ ElectronH0Wannier()

ElectronH0Wannier::ElectronH0Wannier	(	const Eigen::Matrix3d &	directUnitCell_,
		const Eigen::MatrixXd &	bravaisVectors_,
		const Eigen::VectorXd &	vectorsDegeneracies_,
		const Eigen::Tensor< std::complex< double >, 3 > &	h0R_,
		const Eigen::Tensor< std::complex< double >, 4 > *	rMatrix_ = `nullptr`
	)

Parameters

directUnitCell_	the real space unit cell of the crystal in Bohr
bravaisVectors_	the R vectors for the Fourier transform, dimension (3, nRVectors)
vectorsDegeneracies_	the weights of the R vectors for the Fourier transform
h0R_	the Wannier Hamiltonian in real space
rMatrix_	position matrix elements <0m\|r\|nR>

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Member Function Documentation

◆ addShiftedVectors()

void ElectronH0Wannier::addShiftedVectors	(	Eigen::Tensor< double, 3 >	degeneracyShifts_,
		Eigen::Tensor< double, 5 >	vectorsShifts_
	)

Results will be slightly more expensive but more accurate, especially for very small mesh sizes.

Parameters

degeneracyShifts_	vector with the degeneracy of each shifted bravais lattice vector
vectorsShifts_	the shifts to be added to the bravais lattice vectors.

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◆ batchedBuildHamiltonians()

std::vector< Eigen::MatrixXcd > ElectronH0Wannier::batchedBuildHamiltonians ( std::vector< Eigen::Vector3d > & cartesianWavevectors )

Parameters

cartesianWavevectors a std::vector containing the cartesian coordinates of nk wavevectors.

Returns: a vector of hamiltonian matrices in the Bloch representation.

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◆ batchedDiagonalizeFromCoordinates()

std::tuple< std::vector< Eigen::VectorXd >, std::vector< Eigen::MatrixXcd > > ElectronH0Wannier::batchedDiagonalizeFromCoordinates ( std::vector< Eigen::Vector3d > & cartesianWavevectors )

Parameters

cartesianWavevectors a std::vector containing the cartesian coordinates of nk wavevectors.

Returns: tuple with vectors of energies(nk,nb) and eigenvectors(nk,nb,nb).

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◆ batchedDiagonalizeWithVelocities()

std::tuple< std::vector< Eigen::VectorXd >, std::vector< Eigen::MatrixXcd >, std::vector< Eigen::Tensor< std::complex< double >, 3 > > > ElectronH0Wannier::batchedDiagonalizeWithVelocities ( std::vector< Eigen::Vector3d > cartesianCoordinates )

Do diagonalization for a batch of k-points on the CPU.

Parameters

cartesianCoordinates of size(nK,3), contains the cartesian coordinates of the wavevectors at which we want the electronic properties.

Returns: tuple, containing vectors of energies, eigenvectors and velocities at each input wavevector.

Returns the energies (nk, nb), eigenvectors (nk, nb, nb) and velocities (nk, nb, nb, 3) at each k-point.

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◆ diagonalize()

std::tuple< Eigen::VectorXd, Eigen::MatrixXcd > ElectronH0Wannier::diagonalize ( Point & point )

overridevirtual

Energies don't have any reference value, and must be used in connection with a chemical potential.

Parameters

k	a point object with the wavevector. Must have the cartesian coordinates of the wavevector.

Returns: tuple(energies, eigenvectors): the energies are a double vector of size (numBands). Eigenvectors of size (numBands,numBands) are the complex unitary transformation matrix U, connecting the Wannier gauge with the Bloch gauge.

Implements HarmonicHamiltonian.

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◆ diagonalizeFromCoordinates()

std::tuple< Eigen::VectorXd, Eigen::MatrixXcd > ElectronH0Wannier::diagonalizeFromCoordinates ( Eigen::Vector3d & k )

overridevirtual

Same as diagonalize(), but the wavevector coordinates are explicitly passed in input.

Parameters

point the wavevector in cartesian coordinates.

Returns: eigenvalues: the values of quasiparticle energies, a double vector of size numBands.; eigenvectors: a complex matrix of size (numBands,numBands) with the eigenvectors, ordered in columns, computed at the input wavevector.

Implements HarmonicHamiltonian.

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◆ diagonalizeVelocity()

Eigen::Tensor< std::complex< double >, 3 > ElectronH0Wannier::diagonalizeVelocity ( Point & point )

overridevirtual

Parameters

k	a Point object with the wavevector coordinates.

Returns: velocity(numBands,numBands,3): values of the velocity operator for this state, in atomic units.

Implements HarmonicHamiltonian.

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◆ estimateBatchSize()

int ElectronH0Wannier::estimateBatchSize ( const bool & withVelocity )

overridevirtual

Parameters

withVelocity set to true if computing also the velocity operator, which requires more memory

Returns: numBatches: an estimate on how many k-point we can compute in one call of the kokkosBatched functions.

Reimplemented from HarmonicHamiltonian.

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◆ getBerryConnection()

std::vector< Eigen::MatrixXcd > ElectronH0Wannier::getBerryConnection ( Point & point )

wavevectors.

Parameters

point the Point coordinates of the wavevector.

Returns: Berry connection: a generalized Berry connection in the form of a matrix <u_mk| nabla_k |u_nk> for a fixed wavevector. The Berry connection is actually just the diagonal matrix elements.

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◆ getDeviceMemoryUsage()

double ElectronH0Wannier::getDeviceMemoryUsage ( )

protected

Returns: size occupied by Kokkos views, in bytes.

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◆ getNumBands()

int ElectronH0Wannier::getNumBands ( )

overridevirtual

This is a constant for all wavevectors.

Implements HarmonicHamiltonian.

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◆ kokkosBatchedBuildBlochHamiltonian()

StridedComplexView3D ElectronH0Wannier::kokkosBatchedBuildBlochHamiltonian ( const DoubleView2D & cartesianCoordinates )

overridevirtual

Build Hamiltonians for a batch of k-points.

Parameters

cartesianCoordinates a ComplexView2D object of size (nk,3) (must already be on the GPU), containing the cartesian coordinates of a batch of nk wavevectors.

Returns: a View object of size nk,nb,nb containing the nk Hamiltonian matrices.

Implements HarmonicHamiltonian.

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◆ kokkosBatchedDiagonalizeFromCoordinates()

std::tuple< DoubleView2D, StridedComplexView3D > ElectronH0Wannier::kokkosBatchedDiagonalizeFromCoordinates	(	const DoubleView2D &	cartesianCoordinates,
		const bool	withMassScaling = `true`
	)

overridevirtual

Create and diagonalize Hamiltonians for a batch of k-points.

Parameters

cartesianCoordinates a ComplexView2D object of size (nk,3) (must already be on the GPU), containing the cartesian coordinates of a batch of nk wavevectors.

Returns: a tuple of views of energy(nk,nb) and eigenvectors(nk,nb,nb) at each wavevector.

Implements HarmonicHamiltonian.

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◆ kokkosBatchedDiagonalizeWithVelocities()

std::tuple< DoubleView2D, StridedComplexView3D, ComplexView4D > ElectronH0Wannier::kokkosBatchedDiagonalizeWithVelocities ( const DoubleView2D & cartesianCoordinates )

overridevirtual

Build and diagonalize Hamiltonians, with velocities Returns the energies (nk, nb), eigenvectors (nk, nb, nb) and velocities (nk, nb, nb, 3) at each k-point.

Parameters

cartesianCoordinates a ComplexView2D object of size (nk,3) (must already be on the GPU), containing the cartesian coordinates of a batch of nk wavevectors.

Returns: a tuple with energies(nk,nb), eigenvectors(nk,nb,nb) and velocities(nk,nb,nb,3) at each wavevector.

Note that for each k-point, the (nb, nb) eigenvector matrix is column-major, as required by the cuSOLVER routine, hence the StridedLayout.

Implements HarmonicHamiltonian.

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◆ populate() [1/2]

std::tuple< std::vector< Eigen::VectorXd >, std::vector< Eigen::MatrixXcd >, std::vector< Eigen::Tensor< std::complex< double >, 3 > > > ElectronH0Wannier::populate	(	const std::vector< Eigen::Vector3d > &	cartesianCoordinates,
		const bool &	withVelocities,
		const bool &	withEigenvectors
	)

Parameters

cartesianCoordinates	the vector with the list of wavevectors in cartesianCoords
withVelocities	if true, compute the electron velocity operator.
withEigenvectors	if true, stores the Wannier eigenvectors.

Returns: std::tuple: A tuple of std::vectors of eigen objs containing energies, velocities, and eigenvectors of the electronic band structure on the provided points

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◆ populate() [2/2]

FullBandStructure ElectronH0Wannier::populate	(	Points &	fullPoints,
		const bool &	withVelocities,
		const bool &	withEigenvectors,
		const bool	isDistributed = `false`
	)

overridevirtual

Parameters

points	the object with the list/mesh of wavevectors
withVelocities	if true, compute the electron velocity operator.
withEigenvectors	if true, stores the Wannier eigenvectors.

Returns: FullBandStructure: the band structure object containing the complete electronic band structure.

Implements HarmonicHamiltonian.

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Public Member Functions

Protected Member Functions

Protected Attributes

Constructor & Destructor Documentation

◆ ElectronH0Wannier()

Member Function Documentation

◆ addShiftedVectors()

◆ batchedBuildHamiltonians()

◆ batchedDiagonalizeFromCoordinates()

◆ batchedDiagonalizeWithVelocities()

◆ diagonalize()

◆ diagonalizeFromCoordinates()

◆ diagonalizeVelocity()

◆ estimateBatchSize()

◆ getBerryConnection()

◆ getDeviceMemoryUsage()

◆ getNumBands()

◆ kokkosBatchedBuildBlochHamiltonian()

◆ kokkosBatchedDiagonalizeFromCoordinates()

◆ kokkosBatchedDiagonalizeWithVelocities()

◆ populate() [1/2]

◆ populate() [2/2]