  The phonon dynamics in a one dimensional Heisenberg spin chain coupled to
finite-frequency bond phonons is studied. We present the first detailed phonon
spectra for these systems using Quantum Monte Carlo. The quantum phase
transition is dominated by a central peak, yet the renormalisation of the main
phonon branch depends strongly on the bare phonon frequency omega_0. The main
branch remains largely unaffected at omega_0 \gsim J, but it softens completely
when omega_0 is low enough. This is an unusual scenario for a structural phase
transition and was observable only on sufficiently large systems. Approaching
the dimerized phase from finite temperature, the lattice dynamics mirrors the
behavior of a three dimensional system. For the efficient measurement of Greens
functions, we introduce a mapping from the stochastic series expansion to
continuous imaginary time.
