Unitary spin crystals with broken symmetry eigenvectors and spin wave‐mediated interactions

Generalizations of the Heisenberg spin Hamiltonian, Σσ i ⋅σ j are considered. Particles are grouped into molecules and the σ’s are replaced by the generators τ j 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.