Quantum Phase Transition in Antiferromagnetic Heisenberg Chains Coupled to Phonons

We develop an analytical approach based on a unitary transformation to investigate S=1/2 antiferromagnetic Heisenberg chains coupled to phonons, and find a new quantum phase transition at zero temperature. Although the usual phase transition occurs depending on the strengths of the spin-spin and spin-phonon interactions, the phase transition in the present work is induced by a change in the geometrical structure of the spin-phonon interaction. The magnetic properties of the phase transition can be understood in relation to a phase transition that has already been found in the frustrated J1-J2 model.