Quantum lattice fluctuations in a frustrated Heisenberg spin-Peierls chain

TL;DR

This paper investigates a frustrated Heisenberg spin chain coupled to optical phonons, deriving effective models to understand quantum lattice fluctuations and phase diagrams relevant to spin-Peierls systems like CuGeO3.

Contribution

It introduces a combined variational and perturbative approach to derive effective spin Hamiltonians that incorporate phonon effects in different regimes.

Findings

Good agreement with exact diagonalization in the anti-adiabatic regime

Ground-state phase diagrams are mapped out considering frustration effects

Effective models capture dynamical phonon effects approximately

Abstract

As a simple model for spin-Peierls systems we study a frustrated Heisenberg chain coupled to optical phonons. In view of the anorganic spin-Peierls compound CuGeO3 we consider two different mechanisms of spin-phonon coupling. Combining variational concepts in the adiabatic regime and perturbation theory in the anti-adiabatic regime we derive effective spin Hamiltonians which cover the dynamical effect of phonons in an approximate way. Ground-state phase diagrams of these models are determined, and the effect of frustration is discussed. Comparing the properties of the ground state and of low-lying excitations with exact diagonalization data for the full quantum spin phonon models, good agreement is found especially in the anti-adiabatic regime.