Anomalous Entanglement Entropy Scaling in Modified Quantum Scar States of Flatband Systems

Eta pairing state is the exact eigenstate of the flatband-Hubbard model, which shows the anomalous logarithmic scaling of the entanglement entropy. While the eta pairing is an exact eigenstate in the isolated flatband systems, many lattice realization of the flatband such as Lieb and Kagome lattice essentially accompany dispersive bands with band touchings. Here, we examine the deformation of the eta pairing state in the coexistence of dispersive bands. As the finite coupling with the flatband and dispersive band is introduced, we observe the significant corrections in the scaling behavior of the entanglement entropy. Our study provides new insights into the interplay between interaction driven and band structure driven phenomena in flat band systems.