.. _ug_tb_sh_4-5:

************
(4, 5) terms
************

Fifth type of quadlinear terms, in which all four spin operators are associated
with different sites. In this page we imply that
:math:`\boldsymbol{r}_{\mu,\alpha_1}`,
:math:`\boldsymbol{r}_{\mu + \nu_2, \alpha_2}`,
:math:`\boldsymbol{r}_{\mu + \nu_3, \alpha_3}`, and
:math:`\boldsymbol{r}_{\mu + \nu_4, \alpha_4}` are all different.

.. math::
    C_{4, 5}
    \sum_{\substack{\mu, \nu_2, \nu_3, \nu_4 \\ \alpha_1, \alpha_2, \alpha_3, \alpha_4 \\ i_1, i_2, i_3, i_4}}
    J^{i_1, i_2, i_3, i_4}_{\nu_2,\nu_3,\nu_4; \alpha_1,\alpha_2,\alpha_3,\alpha_4}
    S_{\mu, \alpha_1}^{i_1}
    S_{\mu + \nu_2, \alpha_2}^{i_2}
    S_{\mu + \nu_3, \alpha_3}^{i_3}
    S_{\mu + \nu_4, \alpha_4}^{i_4}


Relevant API
============

*   :py:attr:`magnopy.Convention.c45`

    Convention constant.

*   :py:meth:`magnopy.SpinHamiltonian.add`

    Method to add the parameter to the Hamiltonian.

*   :py:meth:`magnopy.SpinHamiltonian.remove`

    Method to remove the parameter from the Hamiltonian.

*   :py:attr:`magnopy.SpinHamiltonian.p45`

    An iterator over the parameters already added to the Hamiltonian.