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A note on the eigenvectors of long-range spin chains and their scalar products

机译:关于远程自旋链的特征向量及其标量的注记   制品

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摘要

In this note, we propose an expression for the eigenvectors and scalarproducts for a class of spin chains with long-range interaction and su(2)symmetry. This class includes the Inozemtsev spin chain as well as the BDS spinchain, which is a reduction of the one-dimensional Hubbard model athalf-filling to the spin sector. The proposal is valid for large spin chainsand is based on the construction of the monodromy matrix using the Dunkloperators. For the Inozemtsev model these operators are known explicitly. Thisconstruction gives in particular the eigenvectors of (an operator closelyrelated to) the dilatation operator of the N=4 gauge theory in the su(2) sectorup to three-loop order, as well as their scalar products. We suggest how thiswill affect the expression for the quasi classical limit of the three-pointfunctions obtained by I. Kostov and how to include the all-loop interaction.
机译:在此注释中,我们提出了具有长距离相互作用和su(2)对称性的一类自旋链的特征向量和标量积的表达式。此类包括Inozemtsev自旋链以及BDS自旋链,这是一维Hubbard模型减少了向自旋扇区的半填充。该建议对大型自旋链有效,并且基于使用Dunkloperators构建单峰矩阵。对于Inozemtsev模型,这些运算符是明确已知的。该构造特别给出了su(2)扇区中N = 4尺度理论的扩张算符(与之密切相关的算符)的特征向量,直至三环阶,以及它们的标量积。我们建议这将如何影响I. Kostov获得的三点函数的拟古典极限的表达式,以及如何包括全环相互作用。

著录项

  • 作者

    Serban, Didina;

  • 作者单位
  • 年度 2013
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  • 原文格式 PDF
  • 正文语种 {"code":"en","name":"English","id":9}
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