Quantized Lattice Dynamic Effects on the Spin-Peierls Transition

TL;DR

This study investigates how quantized phonons influence the spin-Peierls transition in Heisenberg spin chains, revealing a Berezinskii-Kosterlitz-Thouless transition and the impact of phonon dispersion on the critical coupling.

Contribution

It introduces a comprehensive analysis of the spin-Peierls transition considering a spectrum of phonon dispersions, highlighting the effects of phonon dispersion on the transition's critical point.

Findings

Quantum phase transition of BKT type at non-zero coupling

Increase in critical coupling with phonon dispersion

Unreliability of order parameters for transition detection

Abstract

The density matrix renormalization group method is used to investigate the spin-Peierls transition for Heisenberg spins coupled to quantized phonons. We use a phonon spectrum that interpolates between a gapped, dispersionless (Einstein) limit to a gapless, dispersive (Debye) limit. A variety of theoretical probes are used to determine the quantum phase transition, including energy gap crossing, a finite size scaling analysis, bond order auto-correlation functions, and bipartite quantum entanglement. All these probes indicate that in the antiadiabatic phonon limit a quantum phase transition of the Berezinskii-Kosterlitz-Thouless type is observed at a non-zero spin-phonon coupling, $g_{\text c}$. An extrapolation from the Einstein limit to the Debye limit is accompanied by an increase in $g_{\text c}$ for a fixed optical ($q=\pi $) phonon gap. We therefore conclude that the dimerized ground state is more unstable with respect to Debye phonons, with the introduction of phonon dispersion renormalizing the effective spin-lattice coupling for the Peierls-active mode. We also show that the staggered spin-spin and phonon displacement order parameters are unreliable means of determining the transition.