Luttinger liquid versus charge density wave behaviour in the one-dimensional spinless fermion Holstein model

TL;DR

This paper investigates the ground states of the one-dimensional half-filled spinless fermion Holstein model, revealing how phonon frequency influences whether the system behaves as a Luttinger liquid or exhibits charge density wave order.

Contribution

It provides a detailed analysis of the phase behavior using DMRG, highlighting the transition from attractive to repulsive interactions with changing phonon frequency.

Findings

Luttinger liquid exhibits attractive interactions at low phonon frequencies.

Charge density wave state shows long-range order.

Effective charge excitation velocity varies with phonon frequency.

Abstract

We discuss the nature of the different ground states of the half-filled Holstein model of spinless fermions in 1D. In the metallic regime we determine the renormalised effective coupling constant and the velocity of the charge excitations by a density-matrix renormalisation group (DMRG) finite-size scaling approach. At low (high) phonon frequencies the Luttinger liquid is characterised by an attractive (repulsive) effective interaction. In the charge-density wave Peierls-distorted state the charge structure factor scales to a finite value indicating long-range order.