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Diagonalization of the XXZ Hamiltonian by Vertex Operators
We diagonalize the anti-ferroelectric XXZ-Hamiltonian directly in the
thermodynamic limit, where the model becomes invariant under the action of
affine 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 limit ---
the -invariant Thirring model.Comment: 65 page