We recently unveiled that antiferromagnetism (AFM) order can be dominantly induced by the bond Su-Schrieffer-Heeger (SSH) electron-phonon coupling (EPC), which is beyond the conventional wisdom that AFM order is usually driven by strong Coulomb interactions. Nevertheless, many aspects of the interplay between EPC and strong electronic interactions on AFM ordering remain unexplored. Here, we investigate the Su-Schrieffer-Heeger-Hubbard (SSHH) model with bond SSH phonons and on-site Hubbard interactions by large-scale quantum Monte Carlo (QMC) simulations and obtain its ground-state phase diagram for various Hubbard interactions and EPC strength at half filling. Our results show that Hubbard interactions further enhance EPC-induced AFM, especially for small phonon frequency or in adiabatic limit, the regime most relevant to various quantum materials. This could shed further light to understanding the cooperative effect between EPC and electronic correlations in quantum materials.

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• Magnetism
• Phonons
• Antiferromagnets
• Strongly correlated systems
• Quantum Monte Carlo