2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/133372We 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.2 pages, 1 figure, submitted to ICM 2006Strongly Correlated ElectronsStatistical Mechanicstext