The Algebraic Bethe Ansatz and Tensor Networks
  We describe the Algebraic Bethe Ansatz for the spin-1/2 XXX and XXZ Heisenberg chains with open and periodic boundary conditions in terms of tensor networks. These Bethe eigenstates have the structure of Matrix Product States with a conserved number of down-spins. The tensor network formulation suggestes possible extensions of the Algebraic Bethe Ansatz to two dimensions. 
Valentin Murg and Vladimir E. Korepin and Frank Verstraete
cond-mat.str-el quant-ph