We briefly review Bethe Ansatz solutions of the integrable open spin-1/2 XXZ quantum spin chain derived from functional relations obeyed by the transfer matrix at roots of unity.
We review recent results on the Bethe Ansatz solutions for the eigenvalues of the transfer matrix of an integrable open XXZ quantum spin chain using functional relations which the transfer matrix obeys at roots of unity. First, we consider a case where at most two of the boundary parameters {{alpha−,alpha+,beta−,beta+}} are nonzero. A generalization of the Baxter T−Q equation that involves more than one independent Q is described. We use this solution to compute the boundary energy of the chain in the thermodynamic limit. We conclude the paper with a review of some results for the general integrable boundary terms, where all six boundary parameters are arbitrary.
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 i \\pi/(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.
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.