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- W3104454329 abstract "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. We give two derivations of the sub-leading term. Besides a direct derivation by solving a Riemann-Hilbert problem, we give a less rigorous, but more intuitive derivation by field-theoretical methods. For that we represent the Fredholm determinant as an expectation value in a Fock space of chiral fermions and then bosonize. We construct a collective field for the bosonized theory, the short wave-length part of which may be evaluated exactly, while the long wave-length part is amenable to a $1/L$ expansion. Our treatment thus results in a systematic 1/L expansion of structure factors within the Sutherland limit." @default.
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- W3104454329 date "2014-06-02" @default.
- W3104454329 modified "2023-09-25" @default.
- W3104454329 title "Semi-classical analysis of the inner product of Bethe states" @default.
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- W3104454329 doi "https://doi.org/10.1088/1751-8113/47/24/245401" @default.
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