Suppressed superexchange interactions in the cuprates by bond-stretching oxygen phonons

We study a multiorbital Hubbard--Su-Schrieffer-Heeger model for the one-dimensional (1D) corner-shared cuprates in the adiabatic and nonadiabatic limits using exact diagonalization and determinant quantum Monte Carlo. At half filling and in the adiabatic limit, lattice dimerization can be achieved only over a narrow range of couplings slightly below a critical coupling ${g}_{c}$. Beyond this value, the sign of the effective hopping changes, and the lattice becomes unstable. Strong lattice fluctuations replace the dimerization state in the nonadiabatic case. We also examine the model's temperature-dependent uniform and dynamical magnetic susceptibilities and compare them to the results of an effective spin-$1/2$ Heisenberg model. In doing so, we demonstrate that lattice fluctuations induced by the $e$-ph interaction suppress the effective superexchange interaction when $g<{g}_{c}$. Our results elucidate the effect of bond-stretching phonons in the parent cuprate compounds in general and are particularly relevant to 1D cuprates, where strong $e$-ph interactions have recently been inferred.