= Local spin constraint in the Schwinger boson representation
{title2=$(a_n^\dagger a_n+b_n^\dagger b_n)|\psi\rangle=2s|\psi\rangle$}
= Schwinger boson constraint
{c}
{synonym}
The <Schwinger boson representation> satisfies $S_n^2=(N_n/2)(N_n/2+1)$, where $N_n$ is the local total <boson> <number operator>. Thus a prescribed local <spin> $s$ requires the displayed operator constraint at every site. A condition on $\langle N_n\rangle$ alone is insufficient: for $\langle N_n\rangle=2s$, $\langle S_n^2\rangle=s(s+1)+\operatorname{Var}(N_n)/4$. Projecting onto the required <eigenspace> at each site removes the unwanted local <irreducible spin representations>.
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