We diagonalize the anti-ferroelectric XXZ-Hamiltonian directly in the thermodynamic limit, where the model becomes invariant under the action of U q sl(2) . Our method is based on the representation theory of quantum affine algebras, the related vertex operators and KZ equation, and thereby bypasses the usual process of starting from a finite lattice, taking the thermodynamic limit and filling the Dirac sea. From recent results on the algebraic structure of the corner transfer matrix of the model, we obtain the vacuum vector of the Hamiltonian. The rest of the eigenvectors are obtained by applying the vertex operators, which act as particle creation operators in the space of eigenvectors.We check the agreement of our results with those obtained using the Bethe Ansatz in a number of cases, and with others obtained in the scaling limitthe su(2)-invariant Thirring model.
Abstract.A new approach to the correlation functions is presented for the XXZ model in the anti-ferroelectric regime. The method is based on the recent realization of the quantum affine symmetry using vertex operators. With the aid of a boson representation for the latter, an integral formula is found for correlation functions of arbitrary local operators. As a special case it reproduces the spontaneous staggered polarization obtained earlier by Baxter.
The relation between the charge of Lascoux-Schützenberger and the energy function in solvable lattice models is clarified. As an application, A. N. Kirillov's conjecture on the expression of the branching coefficient of sln/sln as a limit of Kostka polynomials is proved.Mathematics Subject Classification (1991). 81R50, 82B23, 17B37, 05A30.
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