The $S_y$ operator is defined as: \begin{equation} S_y = \sum_{\tau} \frac{\imath}{2}\left(-a^{\dagger}_{\tau\uparrow}a^{\phantom{\dagger}}_{\tau\downarrow} + a^{\dagger}_{\tau\downarrow}a^{\phantom{\dagger}}_{\tau\uparrow}\right). \end{equation} The equivalent operator in Quanty is created by:
OppSy = NewOperator("Sy", NF, IndexUp, IndexDn)