Boundary energy of the open XXZ chain from new exact solutions
  Bethe Ansatz solutions of the open spin-1/2 integrable XXZ quantum spin chain at roots of unity with nondiagonal boundary terms containing two free boundary parameters have recently been proposed. We use these solutions to compute the boundary energy (surface energy) in the thermodynamic limit. 
Rajan Murgan, Rafael I. Nepomechie and Chi Shi