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Antiferromagnetism induced by electron-phonon-coupling

Antiferromagnetism (AF) such as Neel ordering is often closely related to Coulomb interactions such as Hubbard repulsion in two-dimensional (2D) systems. Whether Neel AF ordering in 2D can be dominantly induced by electron-phonon couplings (EPC) has not been completely understood. Here, by employing numerically-exact sign-problem-free quantum Monte Carlo (QMC) simulations, we show that optical Su-Schrieffer-Heeger (SSH) phonons with frequency $ω$ and EPC constant $λ$ can induce AF ordering for a wide range of phonon frequency $ω>ω_c$. For $ω<ω_c$, a valence-bond-solid (VBS) order appears and there is a direct quantum phase transition between VBS and AF phases at $ω_c$. The phonon mechanism of the AF ordering is related to the fact that SSH phonons directly couple to electron hopping whose second-order process can induce an effective AF spin exchange. Our results shall shed new lights to understanding AF ordering in correlated quantum materials.