= Two-species uniform boson number state
{title2=$|G\rangle=(A_0^\dagger)^{n_A}(B_0^\dagger)^{n_B}|0\rangle/\sqrt{n_A!n_B!}$}
Two independent <boson> species occupy uniform single-particle modes on $L$ sites, with fixed <occupation numbers> $n_A,n_B$. This differs from a <fixed-number two-mode condensate> whose particles all occupy one superposition of the two modes. Here $\langle a_i^\dagger a_j\rangle=n_A/L$, $\langle b_i^\dagger b_j\rangle=n_B/L$, and the local total <number operator> has <variance> $(n_A+n_B)L^{-1}(1-L^{-1})$. The latter follows from two independent <binomial distributions> with success probability $1/L$. This state satisfies a prescribed <Schwinger boson constraint> only in the mean unless the local <variance> vanishes.
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