Bethe Ansatz for higher spin eight vertex models

Abstract

A generalization of the eight vertex model by means of higher spin representations of the Sklyanin algebra is investigated by the quantum inverse scattering method and the algebraic Bethe Ansatz. Under the well-known string hypothesis low-lying excited states are considered and scattering phase shifts of two physical particles are calculated. The $S$ matrix of two particle states is shown to be proportional to the Baxter's elliptic $R$ matrix with a different elliptic modulus from the original one.

39 pages. AMS-LaTeX with amssymb, amsart. Revision: References and several details are added, typos are corrected

References in corpus (4)

• An elliptic quantum algebra for ${\widehat{sl}}_2$
• Scalar Kinks
• Excitation Scattering in Integrable Models and Hall-Littlewood-Kerov Polynomials
• Generalized $XYZ$ Model Associated to Sklyanin Algebra${}^{\ast }$

Cited by in corpus (15)

• Spin generalization of the Ruijsenaars-Schneider model, non-abelian 2D Toda chain and representations of Sklyanin algebra
• Algebraic Bethe Ansatz for XYZ Gaudin model
• Construction of some missing eigenvectors of the XYZ spin chain at the discrete coupling constants and the exponentially large spectral degeneracy of the transfer matrix
• The eight-vertex model and lattice supersymmetry
• Commuting difference operators with elliptic coefficients from Baxter's vacuum vestors
• Elliptic beta integrals and solvable models of statistical mechanics
• From finite geometry exact quantities to (elliptic) scattering amplitudes for spin chains: the 1/2-XYZ
• New elliptic solutions of the Yang-Baxter equation
• Intertwining operators for Sklyanin algebra and elliptic hypergeometric series
• Continuous biorthogonality of the elliptic hypergeometric function
• The 19-Vertex Model at critical regime $|q|=1$
• Bethe Ansatz for Higher Spin XYZ Models --- Low-lying Excitations ---
• A note on gl_N type-I integrable defects
• The Vertex-Face Correspondence and the Elliptic 6j-symbols
• Finite-dimensional representations of the elliptic modular double