Renormalization of the Spin-Peierls Transition due to Phonon Dynamics

TL;DR

This paper uses a strong-coupling expansion to analyze how phonon dynamics influence the spin-Peierls transition in a spin-1/2 Heisenberg chain, revealing significant renormalization effects in the non-adiabatic regime.

Contribution

It introduces a linked cluster expansion method that preserves full lattice dynamics without truncating phononic Hilbert space for studying spin-phonon coupled systems.

Findings

Spin-phonon coupling renormalizes triplet dispersion.

Large spin gap renormalization occurs only at higher couplings.

Ground state correlations are mainly affected by magnetic frustration.

Abstract

We report results from a systematic strong-coupling expansion of a spin-1/2 Heisenberg chain coupled to Einstein phonons. In the non-adiabatic regime this model is used to describe zero temperature properties of CuGeO3. The linked cluster expansion allows the determination of observables in the thermodynamic limit preserving the full lattice dynamics without a truncation of the phononic Hilbert space. In particular, the spin gap and the dispersion of the elementary triplet excitation are calculated up to 10th order in a dimer expansion. The magnetic structure factor of the ground state is evaluated up to 6th order. We show that the spin-phonon coupling leads to a renormalization of the elementary triplet dispersion. Surprisingly in the non-adiabatic regime a substantial renormalization of the spin gap only sets in at much larger couplings than those proposed for CuGeO3. The ground state magnetic correlations are found to be hardly effected by the spin-phonon coupling, but dominated by the frustrating magnetic interaction in the parameter regime relevant for CuGeO3.