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arXiv:hep-th/0506114 · Journal of Statistical Mechanics Theory and Experiment

Exact results for the σztwo-point function of theXXZchain at Δ = 1/2

N Kitanine, Jean Michel Maillet, N. A. Slavnov, V. Terras

Published Sep 6, 2005• 14 citations
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Abstract

We propose a new multiple-integral representation for the correlation function of the XXZ spin- Heisenberg chain in the disordered regime. We show that for Δ = 1/2 the integrals can be separated and computed exactly. As an example we give the explicit results up to the lattice distance m = 8. It turns out that the answer is given as integer numbers divided by 2 ( m +1) 2 .

DOI
10.1088/1742-5468/2005/09/l09002

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We propose a new multiple-integral representation for the correlation function of the XXZ spin- Heisenberg chain in the disordered regime. We show that for Δ = 1/2 the integrals can be separated and computed exactly. As an example we give the explicit results up to the lattice distance m = 8. It turns out that the answer is given as integer numbers divided by 2 ( m +1) 2 .
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A general approach to the computation of exact correlation functions of lattice quantum integrable models proposed recently is reviewed. It is based on the resolution of the quantum inverse scattering problem. The application of this method to theXXZ Heisenberg spin- 12\tfrac{1}{2}21​ in a magnetic field leads to multiple integral representations of its n-point correlation functions. For zero magnetic field, it gives a proof, in both the massless and massive (anti-ferromagnetic) regimes, of the formulas obtained from the q-deformed KZ equations (massless regime) and the representation theory of the quantum affine algebra Uq(s^l2){\mathcal{U}_q}(\widehat s{l_2})Uq​(sl2​) together with the corner transfer matrix approach (massive regime). We also discuss further problems, related in particular to long distance asymptotics of these correlation functions.
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