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Spin-Peierls transition in the Heisenberg chain with finite-frequency phonons

Anders W. Sandvik·David K. Campbell
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Abstract

We study the spin-Peierls transition in a Heisenberg spin chain coupled to optical bond-phonons. Quantum Monte Carlo results for systems with up to N=256 spins show unambiguously that the transition occurs only when the spin-phonon coupling alpha exceeds a critical value alpha_c. Using sum rules, we show that the phonon spectral function has divergent (for infinite N) weight extending to zero frequency for alpha < alpha_c. The equal-time phonon-phonon correlations decay with distance r as 1/r. This behavior is characteristic for all 0 < alpha < alpha_c and the q=pi phonon does not soften (to zero frequency) at the transition.

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Anders W. Sandvik, David K. Campbell. 1999-02-16. Spin-Peierls transition in the Heisenberg chain with finite-frequency phonons. https://doi.org/10.1103/physrevlett.83.195

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