(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 \(\boldsymbol{r}_{\mu,\alpha_1}\), \(\boldsymbol{r}_{\mu + \nu_2, \alpha_2}\), \(\boldsymbol{r}_{\mu + \nu_3, \alpha_3}\), and \(\boldsymbol{r}_{\mu + \nu_4, \alpha_4}\) are all different.

\[\begin{split}C_{4, 5} \sum_{\substack{\mu, \nu_2, \nu_3, \nu_4 \\ \alpha_1, \alpha_2, \alpha_3, \alpha_4 \\ i_1, i_2, i_3, i_4}} J^{i_1, i_2, i_3, i_4}_{\nu_2,\nu_3,\nu_4; \alpha_1,\alpha_2,\alpha_3,\alpha_4} S_{\mu, \alpha_1}^{i_1} S_{\mu + \nu_2, \alpha_2}^{i_2} S_{\mu + \nu_3, \alpha_3}^{i_3} S_{\mu + \nu_4, \alpha_4}^{i_4}\end{split}\]

Relevant API#