Phonon softening and dispersion in the 1D Holstein model of spinless fermions

TL;DR

This study uses Quantum Monte Carlo simulations to analyze how electron-phonon interactions influence phonon behavior and phase transitions in a one-dimensional Holstein model of spinless fermions, revealing phonon softening, dispersion, and anharmonic features.

Contribution

It provides a detailed quantum Monte Carlo analysis of phonon dynamics and phase transitions in the 1D Holstein model, aligning with previous DMRG results and exploring anharmonic effects.

Findings

Phonon frequency softens near the charge-order transition

Phonon dispersion develops sizable features in the non-adiabatic regime

Anharmonic effects emerge in the phonon propagator

Abstract

We investigate the effect of electron-phonon interaction on the phononic properties in the one-dimensional half-filled Holstein model of spinless fermions. By means of determinantal Quantum Monte Carlo simulation we show that the behavior of the phonon dynamics gives a clear signal of the transition to a charge-ordered phase, and the phase diagram obtained in this way is in excellent agreement with previous DMRG results. By analyzing the phonon propagator we extract the renormalized phonon frequency, and study how it first softens as the transition is approached and then subsequently hardens in the charge-ordered phase. We then show how anharmonic features develop in the phonon propagator, and how the interaction induces a sizable dispersion of the dressed phonon in the non-adiabatic regime.