Lsqr

The $L^2$ operator is defined as: \begin{eqnarray} L^2 = \sum_{m=-l}^{m=l}\sum_{\sigma} && l(l+1) a^{\dagger}_{m,\sigma}a^{\phantom{\dagger}}_{m,\sigma}\\ \nonumber + \sum_{m_1,m_2=-l}^{m_1,m_2=l}\sum_{\sigma_1,\sigma_2}&& \sqrt{l+m_1+1}\sqrt{l-m_1}\\ \nonumber &&\times\,\sqrt{l+m_2+1}\sqrt{l-m_2}\\ \nonumber &&\times \, a^{\dagger}_{m_1+1,\sigma_1}a^{\dagger}_{m_2,\sigma_2}a^{\phantom{\dagger}}_{m_1,\sigma_1}a^{\phantom{\dagger}}_{m_2+1,\sigma_2}. \end{eqnarray} The equivalent operator in Quanty is created by:

Example.Quanty

OppLsqr = NewOperator("Lsqr", NF, IndexUp, IndexDn)