Peierls transition in the quantum spin-Peierls model. - Barford, W; Bursill, R (2005)
We use the density matrix renormalization group method to investigate the role of longitudinal quantized phonons on the Peierls transition in the spin-Peierls model. For both the XY and Heisenberg spin-Peierls model we show that the staggered phonon order parameter scales as sqrt[lambda] (and the dimerized bond order scales as lambda) as lambda-->0 (where lambda is the electron-phonon interaction). This result is true for both linear and cyclic chains. Thus, we conclude that the Peierls transition occurs at lambda=0 in these models. Moreover, for the XY spin-Peierls model we show that the quantum predictions for the bond order follow the classical prediction as a function of inverse chain size for small lambda. We therefore conclude that the zero lambda phase transition is of the mean-field type.