LAUSR

The transfer matrix of the square-lattice eight-vertex model on a strip with L > 1 vertical lines and open boundary conditions is investigated. It is shown that for vertex weights a, b, c, d that obey the relation (a2 + ab)(b2 + ab) = (c2 + ab)(d2 + ab) and appropriately chosen K-matrices K± this transfer matrix possesses the remarkably simple, non-degenerate eigenvalue ΛL = (a + b)2L tr(K+K−). For positive vertex weights, ΛL 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.