We consider a two-spin model, represented classically by a nonlinear
autonomous Hamiltonian system with two degrees of freedom and a nontrivial
integrability condition, and quantum mechanically by a real symmetric
Hamiltonian matrix with blocks of dimensionalities K=l(l+1)/2, l=1,2,... In the
six-dimensional (6D) parameter space of this model, classical integrability is
satisfied on a 5D hypersurface, and level crossings occur on 4D manifolds that
are completely embedded in the integrability hypersurface except for some
lower-D sub-manifolds. Under mild assumptions, the classical integrability
condition can be reconstructed from a purely quantum mechanical study of level
degeneracies in finite-dimensional invariant blocks of the Hamiltonian matrix.
Our conclusions are based on rigorous results for K=3 and on numerical results
for K=6,10.Comment: 8 pages, 3 figure
