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 $% ω$. We confirm the existence of a critical spin-phonon coupling $% α_c\propto ω^{0.7}$ 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 $Δ$ is of order $% ω$. In the classical regime, $Δ>ω$, the mean-field parameters are strongly renormalized by non-adiabatic corrections. This is the first application of the DMRG to phonons.