  We study the low-lying spectrum of the bilinear-biquadratic Heisenberg model
in the dimerized and Haldane phases using a tensor renormalization method. At
the (Takhtajan-Babujian) critical point the finite size spectrum predicted by
the Wess-Zumino-Witten (WZW) model can only partly be confirmed. We find a
singlet-singlet gap which does not fit into the WZW systematics. The results
obtained are compared to Bethe Ansatz, exact diagonalization, and density
matrix renormalization group (DMRG) calculations for specific parameters.
