Antiferromagnetism induced by electron-phonon-coupling

Abstract

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 > ωc. For ω < ωc, a valence-bond-solid (VBS) order appears and there is a direct quantum phase transition between VBS and AF phases at ωc. 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.

Phase Diagram of the Su-Schrieffer-Heeger-Hubbard model on a square lattice

“…( 1) with λ = 0, exhibits an AF phase for any U > 0. Similarly, it was recently established [21,22] that the two-dimensional SSH model, Eq. ( 1) with U = 0, exhibits, at low temperature, an AF phase for small λ and a BOW [20] when λ exceeds a critical value.…”

“…1) for which S AF provided initial evidence. We recall that for g = 0, the system is in the Hubbard AF phase for any U > 0, while for U = 0, the system is in the SSH AF phase [21,22] for small g. The SSH AF at U = 0 clearly has a different mechanism from the traditional two step Hubbard model process of moment formation at energy scale U followed by moment ordering at energy scale J ∼ 4t 2 /U . A close analysis of Fig.…”

“…For the 2D square lattice SSH model at half-filling, it was shown [20] that a finite critical electron-phonon interaction, λ c , is needed to establish the bond-orderwave (BOW) phase, and weak antiferromagnetism was detected [21,22] for λ < λ c despite the absence of U . The cause of this antiferromagnetism is that, on a given bond, only electrons of different spin can tunnel simultaneously, resulting in a lowering of the energy via the electronphonon coupling on the bonds and an increase in the magnitude of the kinetic energy.…”

“…Since the pure SSH Hamiltonian preserves O(4) symmetry, and an AF/CDW/SC degenerate ground state is expected in the anti-adiabatic limit [21,22], it is useful to examine the superconducting structure factor S pairing , the spatial sums of the real space correlations ∆ [31]. These are shown in Fig.…”

“…This occurs even though the system still possesses true long range AF order as demonstrated by a finite size scaling analysis [30]. This is due to the fact that the Hubbard AF and the SSH AF mechanisms are different [21,22]. This new insight into the physics of the SSH-Hubbard Hamiltonian can be thought of as analogous to the well-established crossover from Slater insulator to Mott-Hubbard insulator and from itinerant AF to Heisenberg AF with increasing U in the Hubbard model (g = 0) [29,32,33].…”