Classification of matrix product ground states corresponding to one   dimensional chains of two state sites of nearest neighbor interactions
  A complete classification is given for one dimensional chains with nearest neighbor interactions having two states in each site, for which a matrix product ground state exists. The Hamiltonians and their corresponding matrix product ground states are explicitly obtained. 
Amir H. Fatollahi, Mohammad Khorrami, Ahmad Shariati, Amir   Aghamohammadi
quant-ph cond-mat.stat-mech