Abstract
We derive exactly the number of complex solutions with two down-spins in the massive regime of the periodic spin-1/2 XXZ spin chain of sites. Here we remark that every solution of the Bethe ansatz equations is characterized by a set of quantum numbers. We derive them analytically for all the complex solutions in the sector, which we call two-string solutions. We show that in a region of and the number of two-string solutions is by two larger than the number due to the string hypothesis, i.e. an extra pair of two-strings appears. We determine it exactly and also such regions where two-string solutions collapse for any positive integers . We illustrate the extra and standard two-string solutions numerically. In the sector we show that the string deviations are exponentially small with respect to if is large. We argue that for any finite solution of the spin-1/2 XXX chain there is such a solution of the spin-1/2 XXZ chain that has the same quantum numbers in common with the XXX solution.
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