Abstract
We study the spin-Peierls transition in a Heisenberg spin chain coupled to optical bond-phonons. Quantum Monte Carlo results for systems with up to N=256 spins show unambiguously that the transition occurs only when the spin-phonon coupling alpha exceeds a critical value alpha_c. Using sum rules, we show that the phonon spectral function has divergent (for infinite N) weight extending to zero frequency for alpha < alpha_c. The equal-time phonon-phonon correlations decay with distance r as 1/r. This behavior is characteristic for all 0 < alpha < alpha_c and the q=pi phonon does not soften (to zero frequency) at the transition.
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