The nested Algebraic Bethe Ansatz for the supersymmetric t-J and Tensor Networks

We consider a model of strongly correlated electrons in 1D called the t-J model, which was solved by graded algebraic Bethe ansatz. We use it to design graded tensor networks which can be contracted approximately to obtain a Matrix Product State. As a proof of principle, we calculate observables of ground states and excited states of finite lattices up to $18$ lattice sites.