Interaction-driven spin polaron in itinerant flat-band ferromagnetism

Interaction effects are dramatically enhanced in flat-band systems due to quenched kinetics, facilitating the binding of single excitations into composite quasiparticles. In this work, we present a comprehensive study of spin polarons over the entire momentum and energy space within the Mielke-Tasaki model using projected exact diagonalization. We identify distinct low-energy spin polarons at momenta q=0 and q=\pi, and also find multiple high-energy branches of spin polaron. It is demonstrated that the interaction-induced Hartree dispersion plays a decisive role in determining the momentum sector of low-energy spin polarons. Furthermore, by introducing a finite bandwidth, we unravel the underlying binding mechanisms: the formation of low-energy spin polarons is governed by the conventional virtual exchange mechanism, whereas the high-energy spin polarons arise from a joint effect of the effective attraction and virtual exchange. Our results suggest promising avenues for realizing spin polaron crystals and exploring novel superconducting pairing mechanisms in moir\'e materials like twisted WSe2 and MoTe2.