Free-fermion branches in some quantum spin models

Extensive numerical analysis of the eigenspectra of the SUq(N) invariant Perk-Schultz Hamiltonian shows some simple regularities for a significant part of the eigenspectrum. Inspired by those results we have found two sets of solutions of the associated nested Bethe ansatz equations. The first set is obtained at a special value of the anisotropy (q=exp(iπ(N-1)/N)) and describes, in particular, the ground state and nearby excitations as a sum of free-fermion quasienergies. The second set of solutions provides the energies in the sectors whose number ni of particles of distinct species (i=0, ..., N-1) are less than or equal to unity except for one of the species. For this last set we obtain the eigenspectra of a free-fermion model for arbitrary values of the anisotropy. (author)