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 a XY-spin chain coupled to dispersionless phonons of frequency ω. We confirm the existence of a critical spin-phonon coupling α c ∝ ω 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 ∆ is of order ω. In the classical regime, ∆ > ω, the mean-field parameters are strongly renormalized by non-adiabatic corrections. This is the first application of the DMRG to phonons.