Spin-Phonon Chains with Bond Coupling

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We investigate the antiadiabatic limit of an antiferromagnetic S=1/2 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.