Doped AB_2 Hubbard Chain: Spiral, Nagaoka and RVB States, Phase   Separation and Luttinger Liquid Behavior
  We 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 ($\delta$) 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 $\delta=1/3$. Moreover, for $\delta>1/3$ we observe a crossover, which anticipates the Luttinger liquid behavior for $\delta > 2/3$. 
R. R. Montenegro-Filho and M. D. Coutinho-Filho