(4, 2) terms#
Second type of quadlinear terms, in which three of the four spin operators are associated with the same site, and the fourth spin operator is associated with a different site. In this page we imply that \(\boldsymbol{r}_{\mu,\alpha_1} \neq \boldsymbol{r}_{\mu + \nu_2, \alpha_2}\).
\[\begin{split}C_{4, 2}
\sum_{\substack{\mu, \nu_2, \\ \alpha_1, \alpha_2, \\ i_1, i_2, i_3, i_4}}
\Biggl(
&
J^{i_1, i_2, i_3, i_4}_{0, 0, \nu_2; \alpha_1, \alpha_1, \alpha_1, \alpha_2}
S_{\mu, \alpha_1}^{i_1}
S_{\mu, \alpha_1}^{i_2}
S_{\mu, \alpha_1}^{i_3}
S_{\mu + \nu_2, \alpha_2}^{i_4}
+\\&+
J^{i_1, i_2, i_3, i_4}_{0,\nu_2, 0; \alpha_1,\alpha_1,\alpha_2,\alpha_1}
S_{\mu, \alpha_1}^{i_1}
S_{\mu, \alpha_1}^{i_2}
S_{\mu + \nu_2, \alpha_2}^{i_3}
S_{\mu, \alpha_1}^{i_4}
+\\&+
J^{i_1, i_2, i_3, i_4}_{\nu_2, 0, 0; \alpha_1, \alpha_2, \alpha_1, \alpha_1}
S_{\mu, \alpha_1}^{i_1}
S_{\mu + \nu_2, \alpha_2}^{i_2}
S_{\mu, \alpha_2}^{i_3}
S_{\mu, \alpha_2}^{i_4}
+\\&+
J^{i_1, i_2, i_3, i_4}_{\nu_2, \nu_2, \nu_2; \alpha_1, \alpha_2, \alpha_2, \alpha_2}
S_{\mu, \alpha_1}^{i_1}
S_{\mu + \nu_2, \alpha_2}^{i_2}
S_{\mu + \nu_2, \alpha_2}^{i_3}
S_{\mu + \nu_2, \alpha_2}^{i_4}
\Biggr)\end{split}\]
Relevant API#
-
Convention constant.
-
Method to add the parameter to the Hamiltonian.
magnopy.SpinHamiltonian.remove()Method to remove the parameter from the Hamiltonian.
-
An iterator over the parameters already added to the Hamiltonian.