Semi-classical analysis of the inner product of Bethe states

Understand

We study the inner product of two Bethe states, one of which is taken on-shell, in an inhomogeneous XXX chain in the Sutherland limit, where the number of magnons is comparable with the length L of the chain and the magnon rapidities arrange in a small number of macroscopically large Bethe strings.

• The leading order in the large L limit is known to be expressed through a contour integral of a dilogarithm.
• Here we derive the subleading term.
• Our analysis is based on a new contour-integral representation of the inner product in terms of a Fredholm determinant.