Quantized Lattice Dynamic Effects on the Spin-Peierls Transition

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.

To be published in Phys. Rev. B

References in corpus (2)

• Adiabatic-antiadiabatic crossover in a spin-Peierls chain
• The quantum vs classical aspects of one dimensional electron-phonon systems revisited by the renormalization group method

Cited by in corpus (6)

• Mechanically induced metal-insulator transition in carbyne
• Generalized Moment Method for Gap Estimation and Quantum Monte Carlo Level Spectroscopy
• Effects of spin-phonon coupling in frustrated Heisenberg models
• Quantized Lattice Dynamic Effects on the Peierls transition of the Extended Hubbard Model
• Variational wave functions for the spin-Peierls transition in the Su-Schrieffer-Heeger model with quantum phonons
• Spin Excitation Assisted by Non-Softening Phonon for Spin-Peierls Model