Charge Order in the half-filled bond-Holstein Model

TL;DR

This study uses quantum Monte Carlo simulations to analyze the charge-density-wave transition in a bond-Holstein model, revealing higher transition temperatures and the role of phonon-mediated interactions, with machine learning confirming and extending these findings.

Contribution

It introduces a detailed analysis of the bond-Holstein model showing enhanced CDW tendencies and employs machine learning to identify crossover regimes, advancing understanding of electron-phonon interactions.

Findings

Higher critical temperature for CDW transition compared to site-Holstein model

Phonon-mediated nearest-neighbor electron repulsion enhances charge order

Machine learning confirms transition temperatures and reveals high-temperature crossover

Abstract

We use determinant quantum Monte Carlo to study the half-filled `bond-Holstein' model on a square lattice. We find that the model exhibits a charge-density-wave (CDW) phase transition with a critical temperature $T_\mathrm{cdw}$ considerably higher than that of the canonical `site-Holstein' model. Using a finite-size scaling analysis of the charge structure factor $S_{\rm cdw}$, we obtain $T_\mathrm{cdw}$ to greater than one percent accuracy. At the same time, local observables also show clear signatures consistent with the transition temperatures inferred from our scaling analysis. We attribute the enhanced CDW tendencies to a phonon-mediated nearest-neighbor electron repulsion that is directly proportional to the dimensionless electron-phonon coupling $\lambda$ in the atomic ($t\rightarrow 0$) limit. This behavior contrasts with the site-Holstein case, where the same limit yields only an on-site attraction. We supplement our analysis with results from several unsupervised machine learning methods, which not only confirm our estimates of $T_\mathrm{cdw}$ but also provide insight into the high-temperature crossover between a metallic and bipolaron liquid regime.