Derivation of the matrix product ansatz for the Heisenberg chain from the algebraic Bethe ansatz

作者：Katsura Hosho^*; Maruyama Isao

来源：Journal of Physics A-Mathematical and Theoretical, 2010, 43(17): 175003.

DOI：10.1088/1751-8113/43/17/175003

We derive a matrix product representation of the Bethe ansatz state for the XXX and XXZ spin-1/2 Heisenberg chains using the algebraic Bethe ansatz. In this representation, the components of the Bethe eigenstates are expressed as traces of products of matrices which act on (H) over bar, the tensor product of auxiliary spaces. By changing the basis in (H) over bar, we derive explicit finite-dimensional representations for the matrices. These matrices are the same as those appearing in the recently proposed matrix product ansatz by Alcaraz and Lazo ( 2006 J. Phys. A: Math. Gen. 39 11335) apart from normalization factors. We also discuss the close relation between the matrix product representation of the Bethe eigenstates and the six-vertex model with domain wall boundary conditions (Korepin 1982 Commun. Math. Phys. 86 391) and show that the change of basis corresponds to a mapping from the six-vertex model to the five-vertex model.

• 出版日期2010-4-30
• 单位中国科学院理论物理研究所