On the Semi-Classical Limit of Scalar Products of the XXZ Spin Chain

Abstract

We study the scalar products between Bethe states in the XXZ spin chain with anisotropy $|\Delta |>1$ in the semi-classical limit where the length of the spin chain and the number of magnons tend to infinity with their ratio kept finite and fixed. Our method is a natural yet non-trivial generalization of similar methods developed for the XXX spin chain. The final result can be written in a compact form as a contour integral in terms of Faddeev's quantum dilogarithm function, which in the isotropic limit reduces to the classical dilogarithm function.

references added, journal version

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Cited by in corpus (2)

• Semi-classical quantisation of magnetic solitons in the anisotropic Heisenberg quantum chain
• Semiclassical expansion of the Bethe scalar products in the XXZ spin chain