Lattice dynamics of the Heisenberg chain coupled to finite frequency bond phonons

TL;DR

This study investigates the phonon dynamics in a one-dimensional Heisenberg spin chain coupled to finite-frequency bond phonons using Quantum Monte Carlo, revealing how phonon spectra and phase transitions depend on phonon frequency.

Contribution

First detailed phonon spectra for the Heisenberg chain with bond phonons using Quantum Monte Carlo, including a new mapping for efficient Green's function measurement.

Findings

Main phonon branch remains unaffected at high phonon frequencies

Softening of phonon modes occurs at low phonon frequencies

Lattice dynamics near the phase transition resemble three-dimensional behavior

Abstract

The phonon dynamics in a one dimensional Heisenberg spin chain coupled to finite-frequency bond phonons is studied. We present the first detailed phonon spectra for these systems using Quantum Monte Carlo. The quantum phase transition is dominated by a central peak, yet the renormalisation of the main phonon branch depends strongly on the bare phonon frequency omega_0. The main branch remains largely unaffected at omega_0 \gsim J, but it softens completely when omega_0 is low enough. This is an unusual scenario for a structural phase transition and was observable only on sufficiently large systems. Approaching the dimerized phase from finite temperature, the lattice dynamics mirrors the behavior of a three dimensional system. For the efficient measurement of Greens functions, we introduce a mapping from the stochastic series expansion to continuous imaginary time.