Phonon-induced antiferromagnetism in two dimensions

Antiferromagnetism (AF) such as Neel ordering is often closely related to strong local Coulomb repulsion such as onsite Hubbard repulsion in two-dimensional (2D) systems. Whether Neel AF ordering in 2D can be dominantly induced by electron-phonon couplings has not been completely understood. Here, by employing numerically-exact sign-problem-free quantum Monte Carlo (QMC) simulations, we obtain convincing evidences that Su-Schrieffer-Heeger (SSH) phonons can induce Neel AF ordering on the square lattice for a wide range of phonon frequencies. In the limit of vanishing phonon frequency (namely in the adiabatic limit), the SSH phonons favor a valence-bond solid (VBS) ordering. By increasing the phonon frequency, we show that there is a direct (and possibly deconfined) quantum phase transition from the VBS to AF phases.