Derivation of matrix product states for the Heisenberg spin chain with open boundary conditions
Derivation of matrix product states for the Heisenberg spin chain with open boundary conditions
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具有开放边界条件的海森堡自旋链矩阵积态的推导
DOI：
10.1103/physreve.95.032127
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发表时间：
2017
影响因子：
2.4
通讯作者：
Bolech, C. J.
中科院分区：
文献类型：
--
作者：
Mei, Zhongtao;Bolech, C. J.
利用代数BetheAnsat，我们导出了具有开边界条件的六顶点Heisenberg链的精确Bethe-Ansat态的矩阵乘积表示。在这种表示中，Bethe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。与具有周期边界条件的相同海森堡链的矩阵乘积态相比，精确辅助矩阵的维度被扩大，就好像所考虑的自旋翻转的守恒数目将增加一倍一样。这一结果对任何非嵌套可积模型都是通用的，从我们的推导中可以清楚地看出这一点，我们进一步通过提供一个众所周知的相互作用玻色子气体模型的相同矩阵积态结构的额外例子来说明这一点。与直觉相反的是，尽管有开放的边界，这些矩阵并不依赖于空间坐标，因此它们提出了在有限大小和热力学极限中利用(紧急)平移不变性的一般方法。
Using the algebraic BetheAnsatz, we derive a matrix product representation of the exact Bethe-Ansatzstates of the six-vertex Heisenberg chain (eitherorand spin-) with open boundary conditions. In this representation, the components of the Bethe eigenstates are expressed as traces of products of matrices that act on a tensor product of auxiliary spaces. As compared to the matrix product states of the same Heisenberg chain but with periodic boundary conditions, the dimension of the exact auxiliary matrices is enlarged as if the conserved number of spin-flips considered would have been doubled. This result is generic for any non-nested integrable model, as is clear from our derivation, and we further show this by providing an additional example of the same matrix product state construction for a well-known model of a gas of interacting bosons. Counterintuitively, the matrices do not depend on the spatial coordinate despite the open boundaries, and thus they suggest generic ways of exploiting (emergent) translational invariance both for finite size and in the thermodynamic limit.