ISSN:
1432-0916
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
,
Physics
Notes:
Abstract We diagonalize the anti-ferroelectricXXZ-Hamiltonian directly in the thermodynamic limit, where the model becomes invariant under the action of $$U_q (\widehat{\mathfrak{s}\mathfrak{l}}(2))$$ . 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—thesu(2)-invariant Thirring model.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF02096750
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