Derivation of the matrix product ansatz for the Heisenberg chain from the algebraic Bethe ansatz
Derivation of the matrix product ansatz for the Heisenberg chain from the algebraic Bethe ansatz
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从代数 Bethe ansatz 推导海森堡链的矩阵积 ansatz
DOI：
10.1088/1751-8113/43/17/175003
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发表时间：
2009
期刊：
影响因子：
--
通讯作者：
I. Maruyama
中科院分区：
文献类型：
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作者：
H. Katsura;I. Maruyama
利用代数Bethe变换，我们导出了XXX和XXZ自旋海森堡链Bethe变换态的矩阵乘积表示。在这种表示中，贝特本征态的分量被表示为作用于辅助空间的张量积的矩阵的乘积的迹。通过改变的基础，我们得到明确的有限维表示的矩阵。除了归一化因子之外，这些矩阵与最近由阿尔卡拉兹和Lazo（2006 J. Phys. A：Math.Gen.39 11335）提出的矩阵乘积中出现的那些相同。我们还讨论了Bethe本征态的矩阵乘积表示与具有畴壁边界条件的六顶点模型（Korepin 1982 Commun. Math.Phys.86391），并表明基的变化对应于从六顶点模型到五顶点模型的映射。
We derive a matrix product representation of the Bethe ansatz state for the XXX and XXZ spin- 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 , the tensor product of auxiliary spaces. By changing the basis in , 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.