We know that the spin-1 chain realizes the Haldane phase which is an example of symmetry protected topological (SPT) phases (ie short-range entangled phases with symmetry). The Haldane phase is protected by the $SO(3)$ spin rotation symmetry. If we change the symmetry, we may obtain other possible SPT phases. This motivates us to ask the following question:
What are good examples of quasi 1D insulators with strong spin-orbital interaction?
There are large $U$ Mott insulators and there are small $U$ band insulators. Here, we are interested in both, and like to see examples for both cases.