The $\eta$-pairing states are the exact eigenstates of the hypercubic Hubbard model, which exhibit an anomalous logarithmic scaling of entanglement entropy. It has been shown that $\eta$-pairing states are still exact eigenstates even in multiband systems, provided interband coupling is negligible on the flatband [M. Tovmasyan et al., Phys. Rev. B 94, 245149 (2016); J. Herzog-Arbeitman et al., Commun. Phys. (2026)]. However, typical flatband systems such as Lieb and Kagome lattices often feature band touchings, where interband coupling effects play a role. As an example of such a system, we investigate the deformation of $\eta$-pairing states in the Creutz ladder model with the interband coupling effect. Our results show that the interband coupling introduces effective nonlocal interactions within the flatband. In contrast to previous studies of $\eta$ pairing in isolated flatband systems, here the flatband is coupled to a nearby dispersive band, and we find that the $\eta$-pairing states persist in a modified form with logarithmic entanglement scaling. We observe the suppression of the entanglement entropy and the violation of the spectrum generating algebra. Interestingly, these effects persist even in the limit of infinitesimally small interband coupling. These findings illuminate the robustness and limitations of $\eta$ pairing in realistic setups, offering insights into the physics of interacting flatband systems.

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• Doublon
• Entanglement entropy
• Strongly correlated systems
• Hubbard model