Spectral signatures of the Luttinger liquid to charge-density-wave transition

TL;DR

This paper investigates the spectral properties of a one-dimensional spinless fermion model across different phases, revealing how phonon frequency influences the quantum phase transition from Luttinger liquid to charge-density-wave states.

Contribution

It provides a detailed analysis of electron and phonon spectral functions in various regimes of the Holstein model, highlighting the impact of phonon frequency on the phase transition.

Findings

Spectral functions differ significantly across phases.

Phonon frequency affects the nature of the Peierls transition.

Distinct physics observed in attractive vs. repulsive regimes.

Abstract

Electron- and phonon spectral functions of the one-dimensional, spinless-fermion Holstein model at half filling are calculated in the four distinct regimes of the phase diagram, corresponding to an attractive or repulsive Luttinger liquid at weak electron-phonon coupling, and a band- or polaronic insulator at strong coupling. The results obtained by means of kernel polynomial and systematic cluster approaches reveal substantially different physics in these regimes and further indicate that the size of the phonon frequency significantly affects the nature of the quantum Peierls phase transition.