Quantum phase transition between the spin-Peierls state and the antiferromagnetic state in the TMTTF organic compounds

A competition between the spin-Peierls (SP) state and the antiferromagnetic (AF) state has been examined for the half-filled quasi-one-dimensional electron system coupled with dynamical phonon. By considering the anti-adiabatic limit of phonon, an effective one-dimensional Hamiltonian is derived which includes fluctuations of both the SP state and the AF state. We have shown, by using the renormalization-group method, that a quantum critical point between the SP state and the AF state emerges due to an interference effect of these fluctuations. We discuss the quantum critical behavior between the SP state and the AF state which is predicted in quasi-one-dimensional conductors, TMTTF compounds.