Spin dynamics of dimerized Heisenberg chains

We study numerically the dimerized Heisenberg model with frustration appropriate for the quasi-1D spin-Peierls compound CuGeO$_3$. We present evidence for a bound state in the dynamical structure factor for any finite dimerization $\delta$ and estimate the respective spectral weight. For the homogeneous case ($\delta=0$) we show that the spin-wave velocity $v_s$ is renormalized by the n.n.n. frustration term $\alpha$ as $v_s=\pi/2 J(1-b\alpha)$ with $b\approx1.12$