For special coupling ratios, the one-dimensional (1D) s=1/2 Heisenberg model with antiferromagnetic nearest and next-nearest neighbor interactions has a pure dimer ground state, and the 1D s=1 Heisenberg model with antiferromagnetic bilinear and biquadratic interactions has an exact valence-bond-solid ground state. The recursion method is used to calculate the T=0 spin dynamic structure factor for both models and, for the s=1/2 model, also the dimer dynamic structure factor. New results for line shapes and dynamically relevant dispersions are obtained.
Thermodynamical properties of the one-dimensional
S=1/2 Heisenberg model with dimerized nearest and uniform next-nearest neighbor interactions are studied by the numerically exact quantum transfer-matrix method and the results are applied to
CuGeO3. The Suzuki-Trotter formula is used to obtain a classical system with spin $\ensuremath{\sigma}=3/2$ and effective interactions between nearest neighbors only. The magnetic susceptibility curve is calculated and compared with experimental results in a wide temperature range, revealing the presence of frustration in the model proposed for
CuGeO3. Temperature dependence of the dimerization parameter below the spin-Peierls transition point is also estimated.