Renormalized phonon spectrum of polyacetylene and similar materials

TL;DR

This paper presents a simplified method to compute the renormalized phonon spectrum in polyacetylene-like materials, revealing lattice instabilities and phonon behaviors consistent with prior ab initio studies.

Contribution

It introduces a straightforward approach using the Born-Oppenheimer and harmonic approximations to evaluate phonon spectra, including zero-point energy effects, applicable to higher-dimensional systems.

Findings

Confirmed Kohn anomaly at 2k_F indicating lattice instability

Identified optical and acoustic phonon branches with a gap and softening

Results align with previous ab initio studies for polyacetylene and carbyne

Abstract

Motivated to understand the phonon spectrum renormalization in the ground state of the half-filled SSH model, we use the Born-Oppenheimer approximation together with the harmonic approximation to evaluate the all-to-all real-space ionic force constants generated through the electron-phonon interaction. Using these force constants, we compute the renormalized phonon spectrum and study its behaviour as a function of the Peierls distortion. For the undimerized chain we confirm the presence of a large Kohn anomaly at $2k_F$, signalling a strong lattice instability. For the dimerized chain, we find an optical branch separated by a gap from the acoustic one, while the Kohn anomaly manifests as phonon softening. To find the equilibrium dimerization, we minimize the ground state energy, crucially including the contribution of the renormalized phonon zero-point energy (ZPE). Our results show strong agreement with prior \textit{ab initio} studies for trans-polyacetylene and linear acetylenic carbon (carbyne), validating our method which is much simpler, and moreover can be easily generalized to study other problems in higher dimensions.