sisl.physics.hamiltonian module

Tight-binding class to create tight-binding models.

class sisl.physics.hamiltonian.Hamiltonian(geom, dim=1, dtype=None, nnzpr=None, **kwargs)

Bases: sisl.physics.sparse_physics.SparseOrbitalBZSpin

Hamiltonian object containing the coupling constants between orbitals.

The Hamiltonian object contains information regarding the

• geometry
• coupling constants between orbitals

It contains an intrinsic sparse matrix of the Hamiltonian elements.

Assigning or changing Hamiltonian elements is as easy as with standard numpy assignments:

>>> ham = Hamiltonian(...)
>>> ham.H[1,2] = 0.1

which assigns 0.1 as the coupling constant between orbital 2 and 3. (remember that Python is 0-based elements).

Attributes

H
S
dim	Number of components per element
dkind	Data type of sparse elements (in str)
dtype	Data type of sparse elements
finalized	Whether the contained data is finalized and non-used elements have been removed
geom	Associated geometry
geometry	Associated geometry
nnz	Number of non-zero elements
orthogonal	True if the object is using an orthogonal basis
shape	Shape of sparse matrix
spin	Spin class

Methods

Hk([k, dtype, gauge, format])	Setup the Hamiltonian for a given k-point
Sk([k, dtype, gauge, format])	Setup the overlap matrix for a given k-point
align(other)	See SparseCSR.align for details
construct(func[, na_iR, method, eta])	Automatically construct the sparse model based on a function that does the setting up of the elements
copy([dtype])	A copy of this object
create_construct(R, param)	Create a simple function for passing to the construct function.
cut(seps, axis, *args, **kwargs)	Cuts the sparse orbital model into different parts.
eigh([k, atoms, gauge, eigvals_only, ...])	Returns the eigenvalues of the physical quantity
eigsh([k, n, atoms, gauge, eigvals_only])	Calculates a subset of eigenvalues of the physical quantity (default 10)
eliminate_zeros()	Removes all zero elements from the sparse matrix
empty([keep])	See SparseCSR.empty for details
finalize()	Finalizes the model
fromsp(geom, P[, S])	Read and return the object with possible overlap
iter([local])	Iterations of the orbital space in the geometry, two indices from loop
iter_nnz([atom, orbital])	Iterations of the non-zero elements
read(sile, *args, **kwargs)	Reads Hamiltonian from Sile using read_hamiltonian.
repeat(reps, axis)	Create a repeated sparse orbital object, equivalent to Geometry.repeat
reset([dim, dtype, nnzpr])	The sparsity pattern is cleaned and every thing is reset.
shift(E)	Shift the electronic structure by a constant energy
spsame(other)	Compare two sparse objects and check whether they have the same entries.
sub(atom)	Create a subset of this sparse matrix by only retaining the elements corresponding to the atom
tile(reps, axis)	Create a tiled sparse orbital object, equivalent to Geometry.tile
tocsr(index[, isc])	Return a scipy.sparse.csr_matrix of the specified index
write(sile, *args, **kwargs)	Writes a tight-binding model to the Sile as implemented in the Sile.write_hamiltonian method

Create Hamiltonian model from geometry

Initializes a Hamiltonian using the geom object as the underlying geometry for the tight-binding parameters.

Attributes

H
S
dim	Number of components per element
dkind	Data type of sparse elements (in str)
dtype	Data type of sparse elements
finalized	Whether the contained data is finalized and non-used elements have been removed
geom	Associated geometry
geometry	Associated geometry
nnz	Number of non-zero elements
orthogonal	True if the object is using an orthogonal basis
shape	Shape of sparse matrix
spin	Spin class

Methods

Hk([k, dtype, gauge, format])	Setup the Hamiltonian for a given k-point
Sk([k, dtype, gauge, format])	Setup the overlap matrix for a given k-point
align(other)	See SparseCSR.align for details
construct(func[, na_iR, method, eta])	Automatically construct the sparse model based on a function that does the setting up of the elements
copy([dtype])	A copy of this object
create_construct(R, param)	Create a simple function for passing to the construct function.
cut(seps, axis, *args, **kwargs)	Cuts the sparse orbital model into different parts.
eigh([k, atoms, gauge, eigvals_only, ...])	Returns the eigenvalues of the physical quantity
eigsh([k, n, atoms, gauge, eigvals_only])	Calculates a subset of eigenvalues of the physical quantity (default 10)
eliminate_zeros()	Removes all zero elements from the sparse matrix
empty([keep])	See SparseCSR.empty for details
finalize()	Finalizes the model
fromsp(geom, P[, S])	Read and return the object with possible overlap
iter([local])	Iterations of the orbital space in the geometry, two indices from loop
iter_nnz([atom, orbital])	Iterations of the non-zero elements
read(sile, *args, **kwargs)	Reads Hamiltonian from Sile using read_hamiltonian.
repeat(reps, axis)	Create a repeated sparse orbital object, equivalent to Geometry.repeat
reset([dim, dtype, nnzpr])	The sparsity pattern is cleaned and every thing is reset.
shift(E)	Shift the electronic structure by a constant energy
spsame(other)	Compare two sparse objects and check whether they have the same entries.
sub(atom)	Create a subset of this sparse matrix by only retaining the elements corresponding to the atom
tile(reps, axis)	Create a tiled sparse orbital object, equivalent to Geometry.tile
tocsr(index[, isc])	Return a scipy.sparse.csr_matrix of the specified index
write(sile, *args, **kwargs)	Writes a tight-binding model to the Sile as implemented in the Sile.write_hamiltonian method

H

Hk(k=(0, 0, 0), dtype=None, gauge='R', format='csr', *args, **kwargs)

Setup the Hamiltonian for a given k-point

Creation and return of the Hamiltonian for a given k-point (default to Gamma).

Parameters:

k : array_like

the k-point to setup the Hamiltonian at

dtype : numpy.dtype , optional

the data type of the returned matrix. Do NOT request non-complex data-type for non-Gamma k. The default data-type is ‘numpy.complex128`

gauge : {‘R’, ‘r’}

the chosen gauge, R for cell vector gauge, and r for orbital distance gauge.

format : {‘csr’, ‘array’, ‘dense’, ‘coo’, ...}

the returned format of the matrix, defaulting to the scipy.sparse.csr_matrix, however if one always requires operations on dense matrices, one can always return in numpy.ndarray ('array') or numpy.matrix ('dense').

See also

Sk

Overlap matrix at k

Notes

Currently the implemented gauge for the k-point is the cell vector gauge:

\[H(k) = H_{ij} e^{i k R}\]

where \(R\) is an integer times the cell vector and \(i\), \(j\) are orbital indices.

Another possible gauge is the orbital distance which can be written as

\[H(k) = H_{ij} e^{i k r}\]

where \(r\) is the distance between the orbitals \(i\) and \(j\). Currently the second gauge is not implemented (yet).

static read(sile, *args, **kwargs)

Reads Hamiltonian from Sile using read_hamiltonian.

Parameters:

sile : Sile, str

a Sile object which will be used to read the Hamiltonian and the overlap matrix (if any) if it is a string it will create a new sile using get_sile.

* : args passed directly to read_hamiltonian(,**)

shift(E)

Shift the electronic structure by a constant energy

Parameters:

E : float

the energy (in eV) to shift the electronic structure

write(sile, *args, **kwargs)

Writes a tight-binding model to the Sile as implemented in the Sile.write_hamiltonian method

sisl.physics.hamiltonian.TightBinding

alias of Hamiltonian