2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/155707We present an extensive numerical study of the Hubbard model on the doped AB$_2$ chain, both in the weak coupling and the infinite-U limit. Due to the special unit cell topology, this system displays a rich variety of phases as function of hole doping ($δ$) away from half-filling. Near half-filling, spiral states develop in the weak coupling regime, while Nagaoka itinerant ferromagnetism is observed in the infinite-U limit. For higher doping the system phase-separates before reaching a Mott insulating phase of short-range RVB states at $δ=1/3$. Moreover, for $δ>1/3$ we observe a crossover, which anticipates the Luttinger liquid behavior for $δ> 2/3$.11 pages, 13 figuresStrongly Correlated Electronstext