(3, 2) terms#
Second type of the trilinear terms, in which two spin operators are associated with the same site, and the third one is associated with a different site. In this page we imply that \(\boldsymbol{r}_{\mu,\alpha_1} \neq \boldsymbol{r}_{\mu + \nu_2, \alpha_2}\).
\[\begin{split}C_{3,2}
\sum_{\substack{\mu, \nu_2, \\ \alpha_1, \alpha_2, \\ i_1, i_2, i_3}}
\Biggl(
&
J^{i_1, i_2, i_3}_{0, \nu_2; \alpha_1, \alpha_1, \alpha_2}
S_{\mu, \alpha_1}^{i_1}
S_{\mu, \alpha_1}^{i_2}
S_{\mu + \nu_2, \alpha_2}^{i_3}
+\\&+
J^{i_1, i_2, i_3}_{\nu_2, 0; \alpha_1, \alpha_2, \alpha_1}
S_{\mu, \alpha_1}^{i_1}
S_{\mu + \nu_2, \alpha_2}^{i_2}
S_{\mu, \alpha_1}^{i_3}
+\\&+
J^{i_1, i_2, i_3}_{\nu_2, \nu_2; \alpha_1, \alpha_2, \alpha_2}
S_{\mu, \alpha_1}^{i_1}
S_{\mu + \nu_2, \alpha_2}^{i_2}
S_{\mu + \nu_2, \alpha_2}^{i_3}
\Biggr)\end{split}\]
Relevant API#
-
Convention constant.
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Method to add the parameter to the Hamiltonian.
magnopy.SpinHamiltonian.remove()Method to remove the parameter from the Hamiltonian.
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An iterator over the parameters already added to the Hamiltonian.