On the transfer matrix of the supersymmetric eight-vertex model. II. Open boundary conditions

Hagendorf, Christian [UCL] Liénardy, Jean [UCL]

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 (a^2+ab)(b^2+ab)=(c^2+ab)(d^2+ab) and appropriately chosen K-matrices K± this transfer matrix possesses the remarkably simple, non-degenerate eigenvalue Λ_L=(a+b)^{2L}tr(K_+K_-). For positive vertex weights, Λ_L 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.