EigenstateElectron¶
-
class
sisl.physics.
EigenstateElectron
(state, c, parent=None, **info)[source]¶ Eigen states of electrons with eigenvectors and eigenvalues.
This holds routines that enable the calculation of (projected) density of states, spin moments (spin texture).
Attributes
The data-type of the state (in str)
Data-type for the state
Eigenvalues for each state
Returns the shape of the state
Methods
DOS
(self, E[, distribution])Calculate DOS for provided energies, E.
PDOS
(self, E[, distribution])Calculate PDOS for provided energies, E.
Sk
(self[, format, spin])Retrieve the overlap matrix corresponding to the originating parent structure.
__init__
(self, state, c[, parent])Define a state container with a given set of states and coefficients for the states
align
(self, other[, copy])Align other.state with the angles for this state, a copy of other is returned with rotated elements
asCoefficient
(self)asState
(self)change_gauge
(self, gauge)In-place change of the gauge of the state coefficients
copy
(self)Return a copy (only the coefficients and states are copied),
parent
andinfo
are passed by referencedegenerate
(self, eps)Find degenerate coefficients with a specified precision
expectation
(self, A[, diag])Calculate the expectation value of matrix A
inner
(self[, right, diagonal, align])Return the inner product by \(\mathbf M_{ij} = \langle\psi_i|\psi'_j\rangle\)
inv_eff_mass_tensor
(self[, as_matrix, eps])Calculate inverse effective mass tensor for the states
iter
(self[, asarray])An iterator looping over the states in this system
norm
(self)Return a vector with the norm of each state \(\sqrt{\langle\psi|\psi\rangle}\)
norm2
(self[, sum])Return a vector with the norm of each state \(\langle\psi|\psi\rangle\)
normalize
(self)Return a normalized state where each state has \(|\psi|^2=1\)
occupation
(self[, distribution])Calculate the occupations for the states according to a distribution function
outer
(self[, idx])Return the outer product for the indices idx (or all if
None
) by \(\sum_i|\psi_i\rangle c_i\langle\psi_i|\)phase
(self[, method, return_indices])Calculate the Euler angle (phase) for the elements of the state, in the range \(]-\pi;\pi]\)
rotate
(self[, phi, individual])Rotate all states (in-place) to rotate the largest component to be along the angle phi
sort
(self[, ascending])Sort and return a new
StateC
by sorting the coefficients (default to ascending)spin_moment
(self)Calculate spin moment from the states
sub
(self, idx)Return a new state with only the specified states
velocity
(self[, eps])Calculate velocity for the states
velocity_matrix
(self[, eps])Calculate velocity matrix for the states
wavefunction
(self, grid[, spinor, eta])Expand the coefficients as the wavefunction on grid as-is
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DOS
(self, E, distribution='gaussian')[source]¶ Calculate DOS for provided energies, E.
This routine calls
sisl.physics.electron.DOS
with appropriate arguments and returns the DOS.See
DOS
for argument details.
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PDOS
(self, E, distribution='gaussian')[source]¶ Calculate PDOS for provided energies, E.
This routine calls
PDOS
with appropriate arguments and returns the PDOS.See
PDOS
for argument details.
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Sk
(self, format='csr', spin=None)¶ Retrieve the overlap matrix corresponding to the originating parent structure.
When
self.parent
is a Hamiltonian this will return \(\mathbf S(k)\) for the \(k\)-point these eigenstates originate from- Parameters
- formatstr, optional
the returned format of the overlap matrix. This only takes effect for non-orthogonal parents.
- spinSpin, optional
for non-collinear spin configurations the fake overlap matrix returned will have halve the size of the input matrix. If you want the full overlap matrix, simply do not specify the
spin
argument.
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align
(self, other, copy=False)¶ Align other.state with the angles for this state, a copy of other is returned with rotated elements
States will be rotated by \(\pi\) provided the phase difference between the states are above \(|\Delta\theta| > \pi/2\).
- Parameters
- otherState
the other state to align onto this state
- copybool, optional
sometimes no states require rotation, if this is the case this flag determines whether other will be copied or not
-
asCoefficient
(self)¶
-
asState
(self)¶
-
c
¶
-
change_gauge
(self, gauge)¶ In-place change of the gauge of the state coefficients
The two gauges are related through:
\[\tilde C_j = e^{i\mathbf k\mathbf r_j} C_j\]where \(C_j\) belongs to the gauge
R
and \(\tilde C_j\) is in the gauger
.- Parameters
- gauge{‘R’, ‘r’}
specify the new gauge for the state coefficients
-
copy
(self)¶ Return a copy (only the coefficients and states are copied),
parent
andinfo
are passed by reference
-
degenerate
(self, eps)¶ Find degenerate coefficients with a specified precision
- Parameters
- epsfloat
the precision above which coefficients are not considered degenerate
- Returns
- list of numpy.ndarraya list of indices
-
property
dkind
¶ The data-type of the state (in str)
-
property
dtype
¶ Data-type for the state
-
property
eig
¶ Eigenvalues for each state
-
expectation
(self, A, diag=True)¶ Calculate the expectation value of matrix A
The expectation matrix is calculated as:
\[A_{ij} = \langle \psi_i | \mathbf A | \psi_j \rangle\]If diag is true, only the diagonal elements are returned.
- Parameters
- Aarray_like
a vector or matrix that expresses the operator A
- diagbool, optional
whether only the diagonal elements are calculated or if the full expectation matrix is calculated
- Returns
- numpy.ndarray
a vector if diag is true, otherwise a matrix with expectation values
-
info
¶
-
inner
(self, right=None, diagonal=True, align=True)¶ Return the inner product by \(\mathbf M_{ij} = \langle\psi_i|\psi'_j\rangle\)
- Parameters
- rightState, optional
the right object to calculate the inner product with, if not passed it will do the inner product with itself. This object will always be the left \(\langle\psi_i|\)
- diagonalbool, optional
only return the diagonal matrix \(\mathbf M_{ii}\).
- alignbool, optional
first align right with the angles for this state (see
align
)
- Returns
- numpy.ndarray
a matrix with the sum of outer state products
Notes
This does not take into account a possible overlap matrix when non-orthogonal basis sets are used.
-
inv_eff_mass_tensor
(self, as_matrix=False, eps=0.001)¶ Calculate inverse effective mass tensor for the states
This routine calls inv_eff_mass with appropriate arguments and returns the state inverse effective mass tensor. I.e. for non-orthogonal basis the overlap matrix and energy values are also passed.
Note that the coefficients associated with the
StateCElectron
must correspond to the energies of the states.See
inv_eff_mass_tensor
for details.- Parameters
- as_matrixbool, optional
if true the returned tensor will be a symmetric matrix, otherwise the Voigt tensor is returned.
- epsfloat, optional
precision used to find degenerate states.
Notes
The reason for not inverting the mass-tensor is that for systems with limited periodicities some of the diagonal elements of the inverse mass tensor matrix will be 0, in which case the matrix is singular and non-invertible. Therefore it is the users responsibility to remove any of the non-periodic elements from the matrix.
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iter
(self, asarray=False)¶ An iterator looping over the states in this system
- Parameters
- asarraybool, optional
if true the yielded values are the state vectors, i.e. a numpy array. Otherwise an equivalent object is yielded.
- Yields
- stateState
a state only containing individual elements, if asarray is false
- statenumpy.ndarray
a state only containing individual elements, if asarray is true
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norm
(self)¶ Return a vector with the norm of each state \(\sqrt{\langle\psi|\psi\rangle}\)
- Returns
- numpy.ndarray
the normalization for each state
-
norm2
(self, sum=True)¶ Return a vector with the norm of each state \(\langle\psi|\psi\rangle\)
- Parameters
- sumbool, optional
if true the summed orbital square is returned (a vector). For false a matrix with normalization squared per orbital is returned.
- Returns
- numpy.ndarray
the normalization on each orbital for each state
-
normalize
(self)¶ Return a normalized state where each state has \(|\psi|^2=1\)
This is roughly equivalent to:
>>> state = StateC(np.arange(10), 1) >>> n = state.norm() >>> norm_state = StateC(state.state / n.reshape(-1, 1), state.c.copy()) >>> norm_state.c[0] == 1
- Returns
- statea new state with all states normalized, otherwise equal to this
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occupation
(self, distribution='fermi_dirac')[source]¶ Calculate the occupations for the states according to a distribution function
- Parameters
- distributionstr or func, optional
distribution used to find occupations
- Returns
- numpy.ndarray
len(self)
with occupation values
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outer
(self, idx=None)¶ Return the outer product for the indices idx (or all if
None
) by \(\sum_i|\psi_i\rangle c_i\langle\psi_i|\)- Parameters
- idxint or array_like, optional
only perform an outer product of the specified indices, otherwise all states are used
- Returns
- numpy.ndarraya matrix with the sum of outer state products
-
parent
¶
-
phase
(self, method='max', return_indices=False)¶ Calculate the Euler angle (phase) for the elements of the state, in the range \(]-\pi;\pi]\)
- Parameters
- method{‘max’, ‘all’}
for max, the phase for the element which has the largest absolute magnitude is returned, for all, all phases are calculated
- return_indicesbool, optional
return indices for the elements used when
method=='max'
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rotate
(self, phi=0.0, individual=False)¶ Rotate all states (in-place) to rotate the largest component to be along the angle phi
The states will be rotated according to:
\[S' = S / S^\dagger_{\phi-\mathrm{max}} \exp (i \phi),\]where \(S^\dagger_{\phi-\mathrm{max}}\) is the phase of the component with the largest amplitude and \(\phi\) is the angle to align on.
- Parameters
- phifloat, optional
angle to align the state at (in radians), 0 is the positive real axis
- individualbool, optional
whether the rotation is per state, or a single maximum component is chosen.
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property
shape
¶ Returns the shape of the state
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sort
(self, ascending=True)¶ Sort and return a new
StateC
by sorting the coefficients (default to ascending)- Parameters
- ascendingbool, optional
sort the contained elements ascending, else they will be sorted descending
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spin_moment
(self)¶ Calculate spin moment from the states
This routine calls
spin_moment
with appropriate arguments and returns the spin moment for the states.See
spin_moment
for details.
-
state
¶
-
sub
(self, idx)¶ Return a new state with only the specified states
- Parameters
- idxint or array_like
indices that are retained in the returned object
- Returns
- StateCa new object with a subset of the states
-
velocity
(self, eps=0.0001)¶ Calculate velocity for the states
This routine calls
velocity
with appropriate arguments and returns the velocity for the states. I.e. for non-orthogonal basis the overlap matrix and energy values are also passed.Note that the coefficients associated with the
StateCElectron
must correspond to the energies of the states.See
velocity
for details.- Parameters
- epsfloat, optional
precision used to find degenerate states.
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velocity_matrix
(self, eps=0.0001)¶ Calculate velocity matrix for the states
This routine calls
velocity_matrix
with appropriate arguments and returns the velocity for the states. I.e. for non-orthogonal basis the overlap matrix and energy values are also passed.Note that the coefficients associated with the
StateCElectron
must correspond to the energies of the states.See
velocity_matrix
for details.- Parameters
- epsfloat, optional
precision used to find degenerate states.
-
wavefunction
(self, grid, spinor=0, eta=False)¶ Expand the coefficients as the wavefunction on grid as-is
See
wavefunction
for argument details, the arguments not present in this method are automatically passed from this object.
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