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

Understand

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\to\infty.