Abstract
Generalizations of the Heisenberg spin Hamiltonian, Σσi⋅σj are considered. Particles are grouped into molecules and the σ’s are replaced by the generators τj of the unitary group U(n). Exact eigenvectors are found. A ‘‘vacuum’’ state is given whose U(5) symmetry ‘‘spontaneously’’ breaks for a certain range of potentials. Spin waves superimposed on this vacuum are used to mediate interactions.
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