  Recently, Schmidt et al. proved that the energy spectrum of a Heisenberg spin
system (HSS) is bounded by two parabolas, i.e. lines which depend on the total
spin quantum number S as S(S+1). The prove holds for homonuclear HSSs which
fulfill a weak homogenity condition. Moreover, the extremal values of the exact
spectrum of various HSS which were studied numerically were found to lie on
approximate parabolas, named rotational bands, which could be obtained by a
shift of the boundary parabolas. In view of this, it has been claimed that the
rotational band structure (RBS) of the energy spectrum is a general behavior of
HSSs. Furthermore, since the approximate parabolas are very close to the true
boundaries of the spectrum for the examples discussed, it has been claimed that
the methods allow to predict the detailed shape of the spectrum and related
properties for a general HSS. In this comment I will show by means of examples
that the RBS hypothesis is not valid for general HSSs. In particular, weak
homogenity is neither a necessary nor a sufficient condition for a HSS to
exhibit a spectrum with RBS.
