= Two-spin XY Hamiltonian
{title2=$H=-J(\sigma_1^x\sigma_2^x+\sigma_1^y\sigma_2^y)-h(\sigma_1^z+\sigma_2^z)$}
The two-site quantum version of an <XY model> couples the transverse components of two <spin one-half> degrees of freedom. In the ordered basis $|\uparrow\uparrow\rangle,|\uparrow\downarrow\rangle,|\downarrow\uparrow\rangle,|\downarrow\downarrow\rangle$, its only off-diagonal entries are $H_{23}=H_{32}=-2J$. The parallel states have <energies> $-2h$ and $2h$; the symmetric and antisymmetric opposite-spin combinations have <energies> $-2J$ and $2J$ respectively. The latter is the <singlet state>. The formulas remain valid at accidental degeneracies.
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