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Peierls transition in the quantum spin-Peierls model

William Barford·Robert J. Bursill
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Abstract

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 $\sqrtλ$ (and the dimerized bond order scales as $λ$) as $λ\to 0$ (where $λ$ is the electron-phonon interaction). This result is true for both linear and cyclic chains. Thus, we conclude that the Peierls transition occurs at $λ=0$ 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 $λ$. We therefore conclude that the zero $λ$ phase transition is of the mean-field type.

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William Barford, Robert J. Bursill. 2005-06-06. Peierls transition in the quantum spin-Peierls model. https://doi.org/10.1103/physrevlett.95.137207

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