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

High-temperature superconductivity observed in cuprates remains one of the most captivating phenomena in condensed matter physics. Recent photoemission experiments have provided evidence of a near-neighbor attractive interaction ($V$) in cuprate chains, which may play a crucial role in enhancing pairing mechanisms. To investigate this, we employ the density matrix renormalization group (DMRG) method to calculate the dynamical spin structure factor, $S(q, \omega)$, uncovering a pronounced softening of the two-spinon continuum. This softening, particularly prominent at high momentum, is associated with the renormalization of the superexchange interaction $J$.Our comparison with slave-boson mean-field theory indicates that this softening could serve as a key experimental signature for identifying attractive interactions in cuprates. We propose that resonant inelastic X-ray scattering (RIXS) experiments on thin-film samples could provide direct experimental validation of these findings. RIXS is especially suited for probing spin excitations, as it offers momentum-resolved information that could confirm the predicted softening of the two-spinon continuum due to the attractive interaction ($V$).