Hubbard parent model for Haldane-AKLT S=1 spin chains

S=1 spin models, such as the Haldane and the AKLT, present topological order with gapped bulk excitations and fractional S=1/2 edge states. Here we address the question of how this class of models, generically described with the bilinear biquadratic (BLBQ) spin Hamiltonian, can be obtained as the strong coupling limit of a Hubbard model at half filling. We propose a lattice built with dimers of uncompensated bipartite blocks, that balance each other to give a compensated lattice. In the strong coupling limit of the Hubbard model, the blocks have S=1 and antiferromagneti coupling. At U=0 the model defines a topological insulator with edge states. Using DMRG calculations we map the evolution of the model as we ramp up U. In the large U limit, the model has the same energy levels and correlation functions that a BLBQ S=1 model, which features fractional edge S=1/2 excitations. The crossover between the U=0 non-interacting topological model and the strong coupling limit occurs without the closing of a gap, which indicates that they are topologically equivalent. Our work shows a way to engineer S=1 spin chains with S=1/2 fermions, that could be implemented with quantum dot arrays, cold atoms and planar aromatic hydrocarbons.