Dynamics of quantum spin systems in dimer and valence‐bond‐solid ground states stabilized by competing interactions

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.