Universal Hubbard Models with Arbitrary Symmetry

We propose a general framework that leads to one-dimensional XX and Hubbard models in full generality, based on the decomposition of an arbitrary vector space (possibly infinite dimensional) into a direct sum of two subspaces, the two corresponding orthogonal projectors allowing one to define a R-matrix of a universal XX model, and then of a Hubbard model using a Shastry type construction. The QISM approach ensures integrability of the models, the properties of the obtained R-matrices leading to local Hubbard-like Hamiltonians. In all cases, the energies, the symmetry algebras and the scattering matrices are explicitly determined. The computation of the Bethe Ansatz equations for some sub-sectors of the universal Hubbard theories are determined, while they are fully computed in the XX case. A perturbative calculation in the large coupling regime is also done for the universal Hubbard models.