Boundary energy of the general open XXZ chain at roots of unity
  We have recently proposed a Bethe Ansatz solution of the open spin-1/2 XXZ quantum spin chain with general integrable boundary terms (containing six free boundary parameters) at roots of unity. We use this solution, together with an appropriate string hypothesis, to compute the boundary energy of the chain in the thermodynamic limit. 
Rajan Murgan, Rafael I. Nepomechie and Chi Shi