The $L_x$ operator is defined as: \begin{eqnarray} L_x = \sum_{m=-l}^{m=l}\sum_{\sigma} && \frac{1}{2}\sqrt{l+m+1}\sqrt{l-m}\\ \nonumber &&\times\left(a^{\dagger}_{m+1,\sigma}a^{\phantom{\dagger}}_{m,\sigma} + a^{\dagger}_{m,\sigma}a^{\phantom{\dagger}}_{m+1,\sigma}\right). \end{eqnarray} The equivalent operator in Quanty is created by:
OppLx = NewOperator("Lx", NF, IndexUp, IndexDn)