  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.

Strongly Correlated Electrons