Spin-phonon chains with bond coupling

We investigate the antiadiabatic limit of an antiferromagnetic $S=1/2\mathrm{}$ Heisenberg chain coupled to Einstein phonons via a bond coupling. The flow equation method is used to decouple the spin and the phonon part of the Hamiltonian. In the effective spin model longer range spin-spin interactions are generated. The effective spin chain is frustrated. The resulting temperature-dependent couplings are used to determine the magnetic susceptibility and to determine the phase transition from a gapless state to a dimerized gapped phase. The susceptibilities and the phase diagram obtained via the effective couplings are compared with independently calculated quantum Monte Carlo results.