We propose a Bethe-Ansatz-type solution of the open spin-1/2 integrable XXZ quantum spin chain with general integrable boundary terms and bulk anisotropy values iπ/(p+1), where p is a positive integer. All six boundary parameters are arbitrary, and need not satisfy any constraint. The solution is in terms of generalized T −Q equations, having more than one Q function. We find numerical evidence that this solution gives the complete set of 2 N transfer matrix eigenvalues, where N is the number of spins. 4)

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.

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.