HarmonicHamiltonian Class Reference

Virtual base class for Harmonic Hamiltonian. More...

#include <harmonic.h>

Inheritance diagram for HarmonicHamiltonian:

Public Member Functions
virtual int	getNumBands ()=0
	Returns the total number of phonon branches / electron bands that are available in the interpolator. More...
virtual Particle	getParticle ()=0
	Returns the Particle object to distinguish between electrons and phonons. More...
virtual std::tuple< Eigen::VectorXd, Eigen::MatrixXcd >	diagonalize (Point &point)=0
	Diagonalize the Harmonic Hamiltonian at an arbitrary wavevector. More...
virtual std::tuple< Eigen::VectorXd, Eigen::MatrixXcd >	diagonalizeFromCoordinates (Eigen::Vector3d &k)=0
	Diagonalize the Harmonic Hamiltonian at an arbitrary wavevector. More...
virtual Eigen::Tensor< std::complex< double >, 3 >	diagonalizeVelocity (Point &point)=0
	Computes the velocity operator (if possible, otherwise just its diagonal matrix elements i.e. More...
virtual Eigen::Tensor< std::complex< double >, 3 >	diagonalizeVelocityFromCoordinates (Eigen::Vector3d &coordinates)=0
virtual FullBandStructure	populate (Points &fullPoints, const bool &withVelocities, const bool &withEigenvectors, const bool isDistributed=false)=0
	Method for the construction of the band structure on a grid of of wavevectors of the Brillouin zone. More...
virtual std::tuple< DoubleView2D, StridedComplexView3D, ComplexView4D >	kokkosBatchedDiagonalizeWithVelocities (const DoubleView2D &cartesianCoordinates)=0
void	kokkosBatchedTreatDegenerateVelocities (const DoubleView2D &cartesianCoordinates, const DoubleView2D &resultEnergies, ComplexView4D &resultVelocities, const double &threshold)
virtual StridedComplexView3D	kokkosBatchedBuildBlochHamiltonian (const DoubleView2D &cartesianCoordinates)=0
virtual std::tuple< DoubleView2D, StridedComplexView3D >	kokkosBatchedDiagonalizeFromCoordinates (const DoubleView2D &cartesianCoordinates, const bool withMassScaling=true)=0
virtual int	estimateBatchSize (const bool &withVelocity)
	Estimate how many k-points we can compute on the GPU in one batch. More...

Detailed Description

The subclasses of this base class are the objects responsible for storing the DFT harmonic properties computed on a coarse grid, and containing the methods necessary for interpolating (diagonalizing) such harmonic hamiltonian on a fine grid.

Member Function Documentation

diagonalize()

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

pure virtual

Parameters

point

the Point object describing the wavevector.

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.

Implemented in PhononH0, ElectronH0Wannier, and ElectronH0Fourier.

diagonalizeFromCoordinates()

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

pure virtual

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.

Implemented in ElectronH0Fourier, PhononH0, and ElectronH0Wannier.

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diagonalizeVelocity()

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

pure virtual

the group velocity) of the quasiparticle at the input wavevector. v = \partial energy / \partial k.

Parameters

point

Point object with the input wavevector.

Returns

velocity: a tensor of size(numBands,numBands,3) with the matrix elements of the operator at the given wavevector. (third index is the cartesian direction).

Implemented in PhononH0, ElectronH0Wannier, and ElectronH0Fourier.

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estimateBatchSize()

virtual int HarmonicHamiltonian::estimateBatchSize ( const bool &  withVelocity )

inlinevirtual

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 in PhononH0, and ElectronH0Wannier.

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getNumBands()

virtual int HarmonicHamiltonian::getNumBands ( )

pure virtual

Returns

numBands: integer number of bands.

Implemented in PhononH0, ElectronH0Wannier, and ElectronH0Fourier.

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getParticle()

virtual Particle HarmonicHamiltonian::getParticle ( )

pure virtual

Returns

particle: a Particle object

Implemented in PhononH0, ElectronH0Wannier, and ElectronH0Fourier.

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kokkosBatchedTreatDegenerateVelocities()

void HarmonicHamiltonian::kokkosBatchedTreatDegenerateVelocities	(	const DoubleView2D &	cartesianCoordinates,
		const DoubleView2D &	resultEnergies,
		ComplexView4D &	resultVelocities,
		const double &	threshold
	)

The next part is a bit convoluted because it's tricky to do in parallel We want to build N matrices of size iDegxiDeg containing the velocity degenerate blocks. To this aim, we need two functions funcK, funcB. Such that funcK(iMat), funcB(iMat) return the iK and ib index locating the start of the block that will be diagonalized by the iMat-th matrix

We take advantage of an exclusive scan. Say we have a vector 0 0 0 1 0 0 0 0 1; which spans the bloch states, and 1 locates the beginning of a block of size iDeg that we want to diagonalize. The indices locating the "1", i.e. [3, 8], are given by an exclusive scan: 0 0 0 0 1 1 1 1 1 2 So, scan(ik,ib) = iMat. And from this, I can do the inverse mapping.

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populate()

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

pure virtual

In particular, we save the information for all the bands available to the harmonic hamiltonian.

Parameters

fullPoints	a Points object class over which we will compute the band structure (e.g. FullPoints, or PathPoints)
withVelocities	bool. If set to true, we store the velocity operator.
withEigenvectors	bool. If set to true, we store the eigenvectors

Returns

fullBandStructure: a FullBandStructure object that stores at least the quasiparticle energies and, optionally, velocities and eigenvectors.

Implemented in PhononH0, ElectronH0Wannier, and ElectronH0Fourier.

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