Thermodynamic limit and surface energy of the XXZ spin chain with arbitrary boundary fields

In two previous papers [26,27] the exact solutions of the spin-1/2 chains with arbitrary boundary fields were constructed via the off-diagonal Bethe ansatz (ODBA). Here we introduce a method to approach the thermodynamic limit of those models. The key point is that at a sequence of degenerate points of the crossing parameter eta = eta(m), the off-diagonal Bethe ansatz equations (BAEs) can be reduced to the conventional ones. This allows us to extrapolate the formulae derived from the reduced BAEs to arbitrary eta case with O(N-2) corrections in the thermodynamic limit N -> infinity. As an example the surface energy of the XXZ spin chain model with arbitrary boundary magnetic fields is derived exactly. This approach can be generalized to all the ODBA solvable models. (C) 2014 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/3.0/). Funded by SCOAP(3).