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--- documentation:standard_operators:spin:ssqr [2016/10/05 23:54] – created Maurits W. Haverkort
+++ documentation:standard_operators:spin:ssqr [2025/11/20 03:29] (current) – external edit 127.0.0.1
@@ Line 1: / Line 1: @@
+====== Ssqr ======
+###
+The $S^2$ operator is defined as $S_x^2+S_y^2+S_z^2$ or:
+\begin{eqnarray}
+S^2 &=& \sum_{\tau,\sigma} \frac{3}{4}a^{\dagger}_{\tau,\sigma}a^{\phantom{\dagger}}_{\tau,\sigma} \\
+\nonumber &+& \sum_{\tau_1,\tau_2}\sum_{\sigma_1,\sigma_2} \, -\sigma_1\sigma_2 \, a^{\dagger}_{\tau_1\sigma_1}a^{\dagger}_{\tau_2\sigma_2}a^{\phantom{\dagger}}_{\tau_1\sigma_1}a^{\phantom{\dagger}}_{\tau_2\sigma_2} \\
+\nonumber &&\quad\quad\quad\quad - a^{\dagger}_{\tau_1\uparrow}a^{\dagger}_{\tau_2\downarrow}a^{\phantom{\dagger}}_{\tau_1\downarrow}a^{\phantom{\dagger}}_{\tau_2\uparrow},
+\end{eqnarray}
+with $\sigma$ the spin index which either can be $1/2$ for spin up ($\uparrow$) or $-1/2$ for spin down ($\downarrow$).
+The equivalent operator in Quanty is created by:
+<code Quanty Example.Quanty>
+OppSsqr = NewOperator("Ssqr", NF, IndexUp, IndexDn)
+</code>
+###
+===== Table of contents =====
+{{indexmenu>.#1}}