qml.qchem.spinz

spinz(orbitals)

Computes the total spin projection observable \(\hat{S}_z\).

The total spin projection operator \(\hat{S}_z\) is given by

\[\hat{S}_z = \sum_{\alpha, \beta} \langle \alpha \vert \hat{s}_z \vert \beta \rangle ~ \hat{c}_\alpha^\dagger \hat{c}_\beta, ~~ \langle \alpha \vert \hat{s}_z \vert \beta \rangle = s_{z_\alpha} \delta_{\alpha,\beta},\]

where \(s_{z_\alpha} = \pm 1/2\) is the spin-projection of the single-particle state \(\vert \alpha \rangle\). The operators \(\hat{c}^\dagger\) and \(\hat{c}\) are the particle creation and annihilation operators, respectively.

Parameters

orbitals (str) – Number of spin orbitals. If an active space is defined, this is the number of active spin-orbitals.

Returns

the total spin projection observable \(\hat{S}_z\)

Return type

pennylane.Hamiltonian

Raises

ValueError – If orbitals is less than or equal to 0

Example

>>> orbitals = 4
>>> print(spinz(orbitals))
(
    -0.25 * Z(0)
  + 0.25 * Z(1)
  + -0.25 * Z(2)
  + 0.25 * Z(3)
)

code/api/pennylane.qchem.spinz

 

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