Spin-Peierls transition in the Heisenberg chain with finite-frequency phonons
Sandvik, Anders W.
Campbell, David K.
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Citation (published version)AW Sandvik, DK Campbell. 1999. "Spin-Peierls transition in the Heisenberg chain with finite-frequency phonons." PHYSICAL REVIEW LETTERS, Volume 83, Issue 1, pp. 195 - 198 (4). https://doi.org/10.1103/PhysRevLett.83.195
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 α exceeds a critical value α_c. Using sum rules, we show that the phonon spectral function has divergent (for N→∞) weight extending to zero frequency for α<α_c. The phonon correlations decay with distance r as 1/r. This behavior is characteristic for all 0<α<α_c and the q=π phonon does not soften (to zero frequency) at α=α_c.