Dominant particle-hole contributions to the phonon dynamics in the spinless one-dimensional Holstein model

TL;DR

This paper investigates phonon dynamics in the spinless Holstein model, revealing how electron-phonon coupling induces a phase transition and highlighting the significant role of particle-hole excitations in phonon behavior.

Contribution

It uncovers the dominant particle-hole contributions to phonon dynamics, extending understanding beyond simple phonon mode renormalization in the Holstein model.

Findings

Phonon softening at the Brillouin zone boundary in the adiabatic limit.

Phonon hardening in the anti-adiabatic case.

Electronic particle-hole excitations significantly influence phonon behavior.

Abstract

In the spinless Holstein model at half-filling the coupling of electrons to phonons is responsible for a phase transition from a metallic state at small coupling to a Peierls distorted insulated state when the electron-phonon coupling exceeds a critical value. For the adiabatic case of small phonon frequencies, the transition is accompanied by a phonon softening at the Brillouin zone boundary whereas a hardening of the phonon mode occurs in the anti-adiabatic case. The phonon dynamics studied in this letter do not only reveal the expected renormalization of the phonon modes but also show remarkable additional contributions due to electronic particle-hole excitations.