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

TL;DR

This study investigates how bond-stretching oxygen phonons influence superexchange interactions in 1D cuprates, revealing that lattice fluctuations induced by electron-phonon coupling suppress magnetic superexchange, with implications for understanding cuprate properties.

Contribution

It provides a detailed numerical analysis of the suppression of superexchange interactions by bond-stretching phonons in a multi-orbital Hubbard model, highlighting the role of lattice fluctuations.

Findings

Lattice dimerization occurs only below a critical electron-phonon coupling.

Beyond the critical coupling, the effective hopping sign changes, destabilizing the lattice.

Electron-phonon interactions suppress the superexchange interaction in cuprates.

Abstract

We study a multi-orbital Hubbard--Su-Schrieffer-Heeger model for the one-dimensional (1D) corner-shared cuprates in the adiabatic and nonadiabatic limits using the exact diagonalization and determinant quantum Monte Carlo methods. Our results demonstrate that lattice dimerization can be achieved only over a narrow range of couplings slightly below a critical coupling $g_c$ at half-filling. Beyond this critical coupling, the sign of the effective hopping changes, and the lattice becomes unstable. We also examine the model's temperature-dependent uniform magnetic susceptibility and the dynamical magnetic susceptibility and compare them to the results of an effective spin-$1/2$ Heisenberg model. In doing so, we numerically demonstrate that the lattice fluctuation induced by the $e$-ph interaction suppresses the effective superexchange interaction. 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.