5.6. Bogoliubov representationΒΆ
In the spin system,
the spin indices in the input files of transfer, InterAll,
and correlation functions are specified as those of the Bogoliubov representation.
The spin operators are written by using creation/annihilation operators:
\[\begin{split}S_{i z} &= \sum_{\sigma = -S}^{S} \sigma c_{i \sigma}^\dagger c_{i \sigma}
\\
S_{i}^+ &= \sum_{\sigma = -S}^{S-1}
\sqrt{S(S+1) - \sigma(\sigma+1)}
c_{i \sigma+1}^\dagger c_{i \sigma}
\\
S_{i}^- &= \sum_{\sigma = -S}^{S-1}
\sqrt{S(S+1) - \sigma(\sigma+1)}
c_{i \sigma}^\dagger c_{i \sigma+1}\end{split}\]
