Renormalization of the spin-Peierls transition due to phonon dynamics

We report results from a systematic strong-coupling expansion of a spin-$\frac{1}{2}$ Heisenberg chain coupled to Einstein phonons and a frustrating next-nearest-neighbor spin interaction. It is not obvious which interaction dominates in the regime of small coupling constants. In the non-adiabatic regime ($\hbar \Omega \approx J$) this model is used to describe the zero-temperature properties of CuGeO3. The linked cluster expansion allows the determination of observables in the thermodynamic limit preserving the full lattice dynamics without a truncation of the phononic Hilbert space. We show that the spin-phonon coupling leads to a renormalization of the elementary triplet dispersion. Surprisingly, in the non-adiabatic regime a substantial renormalization of the spin gap only sets in at much larger couplings than those proposed for CuGeO3. The ground-state magnetic correlations are found to be hardly affected by the spin-phonon coupling, but dominated by the frustrating magnetic interaction in the parameter regime relevant for CuGeO3