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We use the density matrix renormalization group (DMRG) to map out the groundstate of a XY-spin chain coupled to dispersionless phonons of frequency $%\omega $. We confirm the existence of a critical spin-phonon coupling $% \alpha_c\propto \omega ^{0.7}$ for the onset of the spin gap bearing the signature ofa Kosterlitz-Thouless transition. We also observe a classical-quantum crossoverwhen the spin-Peierls gap $\Delta $ is of order $% \omega $. In the classicalregime, $\Delta >\omega $, the mean-field parameters are strongly renormalizedby non-adiabatic corrections. This is the first application of the DMRG tophonons.Comment: 10 pages, 5 figures. To be published in PR

Density Matrix Renormalization Group Applied to the Ground State of theXYSpin-Peierls System