Luttinger parameters and momentum distribution function for the half-filled spinless fermion Holstein model: A DMRG approach

TL;DR

This study uses DMRG to analyze the metallic phase of the half-filled spinless fermion Holstein model, revealing contrasting behaviors of the Tomonaga-Luttinger parameter in different regimes and questioning the existence of an attractive metallic state.

Contribution

It provides a detailed DMRG-based analysis of the Luttinger parameter and momentum distribution, highlighting the need to modify scaling relations due to electron-phonon retardation effects.

Findings

K_rho > 1 in intermediate-to-large phonon frequencies

K_rho < 1 in the adiabatic regime

Challenges the existence of an attractive metallic state

Abstract

We reexamine the nature of the metallic phase of the one-dimensional half-filled Holstein model of spinless fermions. To this end we determine the Tomonaga-Luttinger-liquid correlation parameter $K_\rho$ by large-scale density-matrix renormalisation-group (DMRG) calculations, exploiting (i) the leading-order scaling relations between the ground-state energy and the single-particle excitation gap and (ii) the static charge structure factor in the long-wavelength limit. While both approaches give almost identical results for intermediate-to-large phonon frequencies, we find contrasting behaviour in the adiabatic regime: (i) $K_\rho>1$ (attractive) versus (ii) $K_\rho<1$ (repulsive). The latter result for the correlation exponent is corroborated by data obtained for the momentum distribution function $n(k)$, which puts the existence of an attractive metallic state in the spinless fermion Holstein model into question. We conclude that the scaling relation must be modified in the presence of electron-phonon interactions with noticeable retardation.