A new theory of the spin-Peierls transition with special relevance to the experiments on TTFCuBDT

We develop a new theory of the spin-Peierls transition in spin-½ Heisenberg chains, treating the phonons in a mean-field random-phase approximation (RPA) as in previous work, but calculating the relevant response functions of the spin system using the procedure of Luther and Peschel. We show that the RPA on the phonons (and therefore our whole calculation) should be good for the experimentally important system tetrathiafulvalenium bis-cis- (1,2-perfluoromethylethylene-1,2-dithiolato)-copper (TTFCuBDT). It is also exact for a model system in which planes of atoms perpendicular to the chains are constrained by lattice forces to move together: we have derived some exact results for the spin-Peierls transition in this model system. We find a new linear dependence of the transition temperature $T_c$ on the spin-phonon coupling, and an enhancement of $T_c$ and also of the rate of phonon softening above $T_c$. Predictions of some other signatures of the transition, such as the specific-heat jump ratio, are however not much changed from previous work. Exact results are found for the leading dependence of the ground-state energy $E$ and gap $\Delta$ in the excitation spectrum on the lattice distortion $\delta : E\propto {\delta }^{\frac{4}{3}}$, $\Delta \propto {\delta }^{\frac{2}{3}}$.