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We use the two cut-off renormalization group (RG) method to study thespin-Peierls model in one-dimension for the entire phonon frequency range. Weintegrate out the phonon and solve the effective Fermion system via mean fieldand RG methods. We make use of the symmetry that the Neel, dimerization, andspin current order parameters form an SU(2) triplet based on resolving theFermion into left and right movers. We present the phase diagram and discussits implications for the organic charge-transfer salt (TMTTF)$_2$PF$_6$

Analytic approach to the one-dimensional spin-Peierls system in the entire frequency range