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arXiv:1103.4206

On the evaluation of form factors and correlation functions for the integrable spin-s XXZ chains via the fusion method

Tetsuo Deguchi, Chihiro Matsui

Published Mar 22, 2011• 3 citations
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Abstract

Revising the derivation of the previous papers, for the integrable spin-$s$ XXZ chain we express any form factor in terms of a single sum over scalar products of the spin-1/2 XXZ chain. With the revised method we express the spin-$s$ XXZ correlation function of any given entry at zero temperature in terms of a single sum of multiple integrals.

DOI
10.48550/arxiv.1103.4206

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We present a review of the method we have elaborated to compute the correlation functions of the XXZ spin-1/2 Heisenberg chain. This method is based on the resolution of the quantum inverse scattering problem in the algebraic Bethe Ansatz framework, and leads to a multiple integral representation of the dynamical correlation functions. We describe in particular some recent advances concerning the two-point functions: in the finite chain, they can be expressed in terms of a single multiple integral. Such a formula provides a direct analytic connection between the previously obtained multiple integral representations and the form factor expansions for the correlation functions.
We show some symmetry relations among the correlation functions of the integrable higher-spin XXX and XXZ spin chains, where we explicitly evaluate the multiple integrals representing the one-point functions in the spin-1 case.We review the multipleintegral representations of correlation functions for the integrable higher-spin XXZ chains derived in a region of the massless regime including the anti-ferromagnetic point.Here we make use of the gauge transformations between the symmetric and asymmetric R-matrices, which correspond to the principal and homogeneous gradings, respectively, and we send the inhomogeneous parameters to the set of complete 2s-strings.We also give a numerical support for the analytical expression of the one-point functions in the spin-1 case.