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 $S_{\mathrm{cdw}}$, we obtain $T_{\mathrm{cdw}}$ to greater than 1% 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 ($t\to 0$) 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.

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• Charge density waves
• Electron-phonon coupling
• Holstein model
• Machine learning