  Using a new version of the density-matrix renormalization group we determine
the phase diagram of a model of an antiferromagnetic Heisenberg spin chain
where the spins interact with quantum phonons. A quantum phase transition from
a gapless spin-fluid state to a gapped dimerized phase occurs at a non-zero
value of the spin-phonon coupling. The transition is in the same universality
class as that of a frustrated spin chain, which the model maps to in the
anti-adiabatic limit. We argue that realistic modeling of known spin-Peierls
materials should include the effects of quantum phonons.
