The integrable open XXZ chain with broken Z_2 symmetry
  The hamiltonian of an asymmetric diffusion process with injection and ejection of particles at the ends of a chain of finite length is known to be relevant to that of the spin-1/2 XXZ chain with integrable boundary terms. However, the inclusion of boundary sources and sinks of particles breaks the arrow-reversal symmetry necessary for solution via the usual Bethe Ansatz approach. Developments in solving the model in the absence of arrow-reversal symmetry are discussed. 
M.T. Batchelor (ANU)