Matrix product solution to a 2-species TASEP with open integrable   boundaries
  We present an explicit representation for the matrix product ansatz for some two-species TASEP with open boundary conditions. The construction relies on the integrability of the models, a property that constrains the possible rates at the boundaries. The realisation is built on a tensor product of copies of the DEHP algebras. Using this explicit construction, we are able to calculate the partition function of the models. The densities and currents in the stationary state are also computed. It leads to the phase diagram of the models. Depending on the values of the boundary rates, we obtain for each species shock waves, maximal current, or low/high densities phases. 
N. Crampe, M. R. Evans, K. Mallick, E. Ragoucy and M. Vanicat
cond-mat.stat-mech