Form factors of the XXZ Heisenberg spin-1/2 finite chain

Details Form factors of the XXZ Heisenberg spin-1/2 finite chain Form factors of the XXZ Heisenberg spin-1/2 finite chain

1998-07-21

arxiv.org/abs/math-ph/9807020v1

Physics

Mathematical Physics

30 pages, LaTeX2e

Scientific paper

10.1016/S0550-3213(99)00295-3

Form factors for local spin operators of the XXZ Heisenberg spin-1/2 finite chain are computed. Representation theory of Drinfel'd twists for the sl2 quantum affine algebra in finite dimensional modules is used to calculate scalar products of Bethe states (leading to Gaudin formula) and to solve the quantum inverse problem for local spin operators in the finite XXZ chain. Hence, we obtain the representation of the n-spin correlation functions in terms of expectation values(in ferromagnetic reference state) of the operator entries of the quantum monodromy matrix satisfying Yang-Baxter algebra. This leads to the direct calculation of the form factors of the XXZ Heisenberg spin-1/2 finite chain as determinants of usual functions of the parameters of the model. A two-point correlation function for adjacent sites is also derived using similar techniques.

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