Signatures of the Attractive Interaction in Spin Spectra of One-dimensional Cuprate Chains

Identifying the minimal model for cuprates is crucial for explaining the high-$T_c$ pairing mechanism. Recent photoemission experiments have suggested a significant near-neighbor attractive interaction $V$ in cuprate chains, favoring pairing instability. To determine its strength, we systematically investigate the dynamical spin structure factors $S(q,\omega)$ using the density matrix renormalization group. Our analysis quantitatively reveals a notable softening in the two-spinon continuum, particularly evident in the intense spectrum at large momentum. This softening is primarily driven by the renormalization of the superexchange interaction, as determined by a comparison with the slave-boson theory. We also demonstrate the feasibility of detecting this spectral shift in thin-film samples using resonant inelastic x-ray scattering. Therefore, this provides a distinctive fingerprint for the attractive interaction, motivating future experiments to unveil essential ingredients in cuprates.