$\eta$-pairing in a two-band model of spinless fermions

We study the two-band model of spinless fermions in which itinerant fermions interact with localized fermions through the two-particle hybridization. In 1D version, the model has exact solution using the Bethe ansatz. It has been shown that accounting for two-particle hybridization reduces the repulsive interaction between itinerant fermions. In the case of strong interaction, the effective interaction between itinerant fermions is attractive, and $\eta$-pairing of spinless fermions is realized. The proposed pairing mechanism via two-particle hybridization can lead to $p$-superconducting states with $\eta$-pairing. $\eta$-pairing of spinless fermions could explain the phenomenon of high-temperature superconductivity experimentally observed in hydrogen-rich materials at high pressures.