Single-particle excitations and phonon softening in the one-dimensional spinless Holstein model

TL;DR

This paper studies how electron-phonon interactions cause metal-insulator transitions and phonon softening in a one-dimensional spinless Holstein model, using advanced numerical methods to analyze spectral functions and phonon behavior.

Contribution

It introduces a combined use of projector-based renormalization and exact diagonalization techniques to analyze spectral functions and phonon softening in the Holstein model.

Findings

Identification of a metal-insulator transition at finite electron-phonon coupling.

Observation of phonon softening at the Brillouin-zone boundary.

Analysis of spectral functions showing gap opening in the system.

Abstract

We investigate the influence of the electron-phonon coupling in the one-dimensional spinless Holstein model at half-filling using both a recently developed projector-based renormalization method (PRM) and an refined exact diagonalization technique in combination with the kernel polynomial method. At finite phonon frequencies the system shows a metal-insulator transition accompanied by the appearance of a Peierls distorted state at a finite critical electron-phonon coupling. We analyze the opening of a gap in terms of the (inverse) photoemission spectral functions which are evaluated in both approaches. Moreover, the PRM approach reveals the softening of a phonon at the Brillouin-zone boundary which can be understood as precursor effect of the gap formation.