  We extend previous analytical studies of the ground-state phase diagram of a
one-dimensional Heisenberg spin chain coupled to optical phonons, which for
increasing spin-lattice coupling undergoes a quantum phase transition from a
gap-less to a gaped phase with finite lattice dimerisation. We check the
analytical results against established four-block and new two-block density
matrix renormalisation group (DMRG) calculations. Different finite-size scaling
behaviour of the spin excitation gaps is found in the adiabatic and
anti-adiabatic regimes.
