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The European Physical Journal B

Eigenvalues of the eight-vertex model transfer matrix and the spectrum of theXYZ Hamiltonian

Andreas Kl�mper, J. Zittartz

Published Dec 1, 1988• 39 citations
Publisher
DOI
10.1007/bf01313936

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The eigenvalues of the Corner Transfer Matrix Hamiltonian associated to the elliptic RRR matrix of the eight vertex free fermion model are computed in the anisotropic case for magnetic field smaller than the critical value. An argument based on generating functions is given, and the results are checked numerically. The spectrum consists of equally spaced levels.
Abstract The transfer matrix of the square-lattice eight-vertex model on a strip with vertical lines and open boundary conditions is investigated. It is shown that for vertex weights that obey the relation and appropriately chosen K -matrices this transfer matrix possesses the remarkably simple, non-degenerate eigenvalue . For positive vertex weights, is shown to be the largest transfer-matrix eigenvalue. The corresponding eigenspace is equal to the space of the ground states of the Hamiltonian of a related XYZ spin chain. An essential ingredient in the proofs is the supersymmetry of this Hamiltonian.