(4, 3) terms#

Third type of quadlinear terms, in which two of the four spin operators are associated with the first site and the other two spin operators are associated with the second site. In this page we imply that \(\boldsymbol{r}_{\mu,\alpha_1} \neq \boldsymbol{r}_{\mu + \nu_2, \alpha_2}\).

\[\begin{split}C_{4, 3} \sum_{\substack{\mu, \nu_2, \\ \alpha_1, \alpha_2, \\ i_1, i_2, i_3, i_4}} \Biggl( & J^{i_1, i_2, i_3, i_4}_{0, \nu_2, \nu_2; \alpha_1, \alpha_1, \alpha_2, \alpha_2} S_{\mu, \alpha_1}^{i_1} S_{\mu, \alpha_1}^{i_2} S_{\mu + \nu_2, \alpha_2}^{i_3} S_{\mu + \nu_2, \alpha_2}^{i_4} +\\&+ J^{i_1, i_2, i_3, i_4}_{\nu_2, 0, \nu_2; \alpha_1, \alpha_2, \alpha_1, \alpha_2} S_{\mu, \alpha_1}^{i_1} S_{\mu + \nu_2, \alpha_2}^{i_2} S_{\mu, \alpha_1}^{i_3} S_{\mu + \nu_2, \alpha_2}^{i_4} +\\&+ J^{i_1, i_2, i_3, i_4}_{\nu_2, \nu_2, 0; \alpha_1, \alpha_2, \alpha_2, \alpha_1} S_{\mu, \alpha_1}^{i_1} S_{\mu + \nu_2, \alpha_2}^{i_2} S_{\mu + \nu_2, \alpha_2}^{i_3} S_{\mu, \alpha_1}^{i_4} \Biggr)\end{split}\]

Relevant API#