The quantum inverse problem method and the XYZ Heisenberg model

L A Takhtadzhan, L. D. Faddeev

Guo-Hui Yang, Xiang Yang Miao, Jun Feng Zhang

L A Takhtadzhan, Lyudvig Dmitrievich Faddeev

CONTENTS Introduction § 1. Classical statistical physics on a two-dimensional lattice and quantum mechanics on a chain § 2. Connection with the inverse problem method § 3. The six-vertex model § 4. Generating vectors and permutation relations § 5. The general Bethe Ansatz § 6. Integral equations Conclusion Appendix 1 Appendix 2 References

Evgeny Konstantinovich Sklyanin, Leon Armenovich Takhtadzhyan, Lyudvig Dmitrievich Faddeev

Kiyoshi Sogo, Miki Wadati

The Lax pair for spin 1/2 Heisenberg XYZ model is presented. This gives a basis for the quantum inverse scattering method. A generalization of the Yang-Baxter relation to arbitrary spin is presented through the factorized S-matrix theory. An equivalent vertex model is solved exactly by the quantum inverse scattering method.