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 $\delta > 2/3$.Comment: 11 pages, 13 figure

Frustration-induced quantum phase transitions in a quasi-one-dimensional ferrimagnet: Hard-core boson map and the Ton ks-Girardeau limit

We provide evidence of a superfluid-insulator transition (SIT) of magnons in a quasi-one-dimensional quantum ferrimagnet with {\it isotropic} competing antiferromagnetic spin interactions. This SIT occurs between two distinct ferrimagnetic phases due to the frustration-induced closing of the gap to a magnon excitation. It thus causes a coherent superposition of singlet and triplet states at lattice unit cells and a power-law decay on the staggered spin correlation function along the transverse direction to the spontaneous magnetization. A hard-core boson map suggests that asymptotically close to the SIT the magnons attain the Tonks-Girardeau limit. The quantized nature of the condensed singlets is observed before a first-order transition to a singlet magnetic spiral phase accompanied by critical antiferromagnetic ordering. In the limit of strong frustration, the system undergoes a decoupling transition to an isolated gapped two-leg ladder and a critical single linear chain

Magnetism and Electronic Correlations in Quasi-One-Dimensional Compounds

In this contribution on the celebration of the 80th birthday anniversary of Prof. Ricardo Ferreira, we present a brief survey on the magnetism of quasi-one-dimensional compounds. This has been a research area of intense activity particularly since the first experimental announcements of magnetism in organic and organometallic polymers in the mid 80s. We review experimental and theoretical achievements on the field, featuring chain systems of correlated electrons in a special AB2 unit cell structure present in inorganic and organic compounds