= Quantum XY chain
{title2=$H=-J\sum_n(S_n^xS_{n+1}^x+S_n^yS_{n+1}^y)$}
A one-dimensional quantum <spin> model with transverse <XY exchange interactions>; $J>0$ is the ferromagnetic sign in the displayed convention. Unlike the classical <XY model>, its site variables are noncommuting <spin operators> in a fixed <irreducible spin representation>. With <periodic boundary conditions> and $L\ge2$, $H=-\tfrac J2\sum_n(S_n^+S_{n+1}^-+S_n^-S_{n+1}^+)$. It preserves total $S^z$ and the associated global <U(1)> <symmetry>.
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