Analytical approach to the quantum-phase transition in the one-dimensional spinless Holstein model

TL;DR

This paper presents an analytical study of the quantum-phase transition in a one-dimensional spinless Holstein model, revealing how electron-phonon interactions induce a metal-insulator transition with characteristic phonon softening.

Contribution

It introduces a projector-based renormalization method to analyze the transition within a unified theoretical framework for different fillings.

Findings

Metal-insulator transition at half-filling with phonon softening at zone boundary

Transition characterized by a gap opening in the electronic spectrum

Different phonon softening behavior at other fillings

Abstract

We study the one-dimensional Holstein model of spinless fermions interacting with dispersion-less phonons by using a recently developed projector-based renormalization method (PRM). At half-filling the system shows a metal-insulator transition to a Peierls distorted state at a critical electron-phonon coupling where both phases are described within the same theoretical framework. The transition is accompanied by a phonon softening at the Brillouin zone boundary and a gap in the electronic spectrum. For different filling, the phonon softening appears away from the Brillouin zone boundary and thus reflects a different type of broken symmetry state.