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

TL;DR

This study investigates the spin-Peierls transition in a Heisenberg chain with optical phonons, revealing a critical coupling threshold and specific phonon spectral behaviors through quantum Monte Carlo simulations.

Contribution

It demonstrates that the transition occurs only above a critical spin-phonon coupling and characterizes phonon spectral properties near the transition point.

Findings

Transition occurs only when coupling exceeds critical value

Phonon spectral function shows divergence at zero frequency below critical coupling

Phonon correlations decay as 1/r, with no softening at the transition

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.