Sum rules for the supersymmetric eight-vertex model
(2021) Journal of Statistical Mechanics: Theory and Experiment — p. 23102 (2021)
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- Abstract
- The eight-vertex model on the square lattice with vertex weights a,b,c,d obeying the relation (a^2+ab)(b^2+ab)=(c^2+ab)(d^2+ab) is considered. Its transfer matrix with L=2n+1,n⩾0, vertical lines and periodic boundary conditions along the horizontal direction has the doubly-degenerate eigenvalue Θ_n=(a+b)^{2n+1}. A basis of the corresponding eigenspace is investigated. Several scalar products involving the basis vectors are computed in terms of a family of polynomials introduced by Rosengren and Zinn-Justin. These scalar products are used to find explicit expressions for particular entries of the vectors. The proofs of these results are based on the generalisation of the eigenvalue problem for Θ_n to the inhomogeneous eight-vertex model.
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Brasseur, S., & Walmsley Hagendorf, C. (2021). Sum rules for the supersymmetric eight-vertex model. Journal of Statistical Mechanics: Theory and Experiment, 23102. https://doi.org/10.1088/1742-5468/abda28 (Original work published 2021)