On the transfer matrix of the supersymmetric eight-vertex model. II. Open boundary conditions
(2020) Journal of Statistical Mechanics: Theory and Experiment —
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- Abstract
- 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.
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Walmsley Hagendorf, C., & Liénardy, J. (2020). On the transfer matrix of the supersymmetric eight-vertex model. II. Open boundary conditions. Journal of Statistical Mechanics: Theory and Experiment. https://hdl.handle.net/2078.5/99375