The $L_z$ operator is defined as: \begin{eqnarray} L_z = \sum_{m=-l}^{m=l}\sum_{\sigma} m a^{\dagger}_{m,\sigma}a^{\phantom{\dagger}}_{m,\sigma}. \end{eqnarray} The equivalent operator in Quanty is created by:
OppLz = NewOperator("Lz", NF, IndexUp, IndexDn)