Peierls Dimerization with Nonadiabatic Spin-Phonon Coupling

We study the magnetic properties of a frustrated Heisenberg spin chain with a dynamic spin-phonon interaction. Using Lanczos diagonalization that preserves the full lattice dynamics, we explore the nonadiabatic regime with phonon frequencies comparable to the exchange coupling energy, which is, for example, the relevant limit for the spin-Peierls compound $\mathrm{CuGeO}{}_3$. Compared to the static limit of an alternating spin chain, the magnetic properties are strongly renormalized due to the coupled dynamics of spin and lattice degrees of freedom. The dependence of the magnitude of the spin-triplet excitation gap changes from a strong to a weak dimerization with increasing phonon frequencies implying the necessity to include dynamic effects in a quantitative description of the spin-Peierls state in $\mathrm{CuGeO}{}_3$.