Bethe ansatz for higher spin eight-vertex models

1995/04/30 by Takashi Takebe · 2 citations
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Nonlinear Waves and Solitons #cond-mat #hep-th #math.QA #q-alg

paper · pdf · doi:10.1088/0305-4470/28/23/019

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

arxiv created 1995/07/14 · openalex publication_date 1995/12/07 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30

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 Baxter`s (1972) elliptic R-matrix with a different elliptic modulus from the original one.

Citations

• Eight-vertex model in lattice statistics and one-dimensional anisotropic heisenberg chain. I. Some fundamental eigenvectors
• Eight-vertex model in lattice statistics and one-dimensional anisotropic heisenberg chain. III. Eigenvectors of the transfer matrix and hamiltonian
• Eight-vertex model in lattice statistics and one-dimensional anisotropic heisenberg chain. II. Equivalence to a generalized ice-type lattice model
• Generalized XYZ Model Associated to Sklyanin Algebra^*

Cited by

• Commuting difference operators with elliptic coefficients from Baxter's vacuum vectors
• Algebraic bethe ansatz for the XYZ Gaudin model