Density matrix renormalization group applied to the ground state of the XY spin-Peierls system

We use the density matrix renormalization group (DMRG) to map out the ground state of an XY spin chain coupled to dispersionless phonons of frequency omega. We confirm the existence of a critical spin-phonon coupling alpha(c) proportional to omega(0.7) for the onset of the spin gap bearing the signature of a Kosterlitz-Thouless transition. We also observe a classical-quantum crossover when the spin-Peierls gap Delta is of order omega. In the classical regime Delta > omega, the mean-field parameters are strongly renormalized by nonadiabatic corrections. This is the first application of the DMRG to phonons.