Peierls transition in the quantum spin-Peierls model

TL;DR

This study uses the density matrix renormalization group method to analyze how quantized phonons influence the Peierls transition in spin-Peierls models, revealing a transition at zero electron-phonon coupling and mean-field behavior.

Contribution

It demonstrates that the Peierls transition occurs at zero coupling in both XY and Heisenberg models using quantum phonons, extending classical predictions to quantum regimes.

Findings

Peierls transition occurs at zero electron-phonon coupling ($\,\lambda=0$)

Bond order scales as $\,\lambda$ near transition, indicating mean-field behavior

Quantum predictions match classical results for small $\,\lambda$ in XY model

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 $\sqrt{\lambda}$ (and the dimerized bond order scales as $\lambda$) as $\lambda \to 0$ (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.