On the transfer matrix of the supersymmetric eight-vertex model. I. Periodic boundary conditions
(2018) Journal of Statistical Mechanics: Theory and Experiment — Vol. 2018, n° 03, p. 33106 (2018)
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- Abstract
- The square-lattice eight-vertex model with vertex weights a,b,c,d obeying the relation (a2+ab)(b2+ab)=(c2+ab)(d2+ab) and periodic boundary conditions is considered. It is shown that the transfer matrix of the model for L=2n+1 vertical lines and periodic boundary conditions along the horizontal direction possesses the doubly degenerate eigenvalue Θn=(a+b)2n+1. This proves a conjecture by Stroganov from 2001. The proof uses the supersymmetry of a related XYZ spin-chain Hamiltonian. The eigenstates of the transfer matrix corresponding to Θn are shown to be the ground states of the spin-chain Hamiltonian. Moreover, for positive vertex weights Θn is the largest eigenvalue of the transfer matrix.
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Walmsley Hagendorf, C., & Liénardy, J. (2018). On the transfer matrix of the supersymmetric eight-vertex model. I. Periodic boundary conditions. Journal of Statistical Mechanics: Theory and Experiment, 2018(03), 33106. https://doi.org/10.1088/1742-5468/aab01d (Original work published 2018)