(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#