(4, 4) terms#
Forth type of quadlinear terms, in which two of the four spin operators are associated with the first site, one spin operator is associated with the second site and one spin operator is associated with the third site. In this page we imply that \(\boldsymbol{r}_{\mu,\alpha_1}\), \(\boldsymbol{r}_{\mu + \nu_2, \alpha_2}\), and \(\boldsymbol{r}_{\mu + \nu_3, \alpha_3}\) are all different.
\[\begin{split}C_{4, 4}
\sum_{\substack{\mu, \nu_2, \nu_3, \\ \alpha_1, \alpha_2, \alpha_3, \\ i_1, i_2, i_3, i_4}}
\Biggl(
&
J^{i_1, i_2, i_3, i_4}_{0,\nu_2,\nu_3; \alpha_1,\alpha_1,\alpha_2,\alpha_3}
S_{\mu, \alpha_1}^{i_1}
S_{\mu, \alpha_1}^{i_2}
S_{\mu + \nu_2, \alpha_2}^{i_3}
S_{\mu + \nu_3, \alpha_3}^{i_4}
+\\&+
J^{i_1, i_2, i_3, i_4}_{\nu_2, 0,\nu_3; \alpha_1,\alpha_2,\alpha_1,\alpha_3}
S_{\mu, \alpha_1}^{i_1}
S_{\mu + \nu_2, \alpha_2}^{i_2}
S_{\mu, \alpha_1}^{i_3}
S_{\mu + \nu_3, \alpha_3}^{i_4}
+\\&+
J^{i_1, i_2, i_3, i_4}_{\nu_2,\nu_3,0; \alpha_1,\alpha_2,\alpha_3,\alpha_1}
S_{\mu, \alpha_1}^{i_1}
S_{\mu + \nu_2, \alpha_2}^{i_2}
S_{\mu + \nu_3, \alpha_3}^{i_3}
S_{\mu, \alpha_1}^{i_4}
+\\&+
J^{i_1, i_2, i_3, i_4}_{\nu_2,\nu_2,\nu_3; \alpha_1,\alpha_2,\alpha_2,\alpha_3}
S_{\mu, \alpha_1}^{i_1}
S_{\mu + \nu_2, \alpha_2}^{i_2}
S_{\mu + \nu_2, \alpha_2}^{i_3}
S_{\mu + \nu_3, \alpha_3}^{i_4}
+\\&+
J^{i_1, i_2, i_3, i_4}_{\nu_2,\nu_3,\nu_2; \alpha_1,\alpha_2,\alpha_3,\alpha_2}
S_{\mu, \alpha_1}^{i_1}
S_{\mu + \nu_2, \alpha_2}^{i_2}
S_{\mu + \nu_3, \alpha_3}^{i_3}
S_{\mu + \nu_2, \alpha_2}^{i_4}
+\\&+
J^{i_1, i_2, i_3, i_4}_{\nu_2,\nu_3,\nu_3; \alpha_1,\alpha_2,\alpha_3,\alpha_3}
S_{\mu, \alpha_1}^{i_1}
S_{\mu + \nu_2, \alpha_2}^{i_2}
S_{\mu + \nu_3, \alpha_3}^{i_3}
S_{\mu + \nu_3, \alpha_3}^{i_4}
\Biggr)\end{split}\]
Relevant API#
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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.