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

Abstract

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 . We confirm the existence of a critical spin-phonon coupling 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 . In the classical regime, $\Delta >\omega$, the mean-field parameters are strongly renormalized by non-adiabatic corrections. This is the first application of the DMRG to phonons.

10 pages, 5 figures. To be published in PRL