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摘要翻译：
近年来研究表明，非对称排斥问题的本征函数及其几种推广以及大量的量子链族，如各向异性Heisenberg模型、Fateev-Zamolodchikov模型、Izergin-Korepin模型、Sutherland模型、t-J模型、Hubbard模型等，都可以用矩阵积表示。与本征值和特征向量为平面波组合的坐标系Bethe ansatz不同，在这种坐标系中，本征函数的分量是通过适当定义的矩阵的代数性质得到的。本文给出了具有周期边界条件的六顶点模型的矩阵积ansatz的一个表达式，它是二维可积性的典型例子。值得注意的是，我们对六顶点模型的研究与所有用Bethe ansatz精确求解的模型也可以用适当的矩阵乘积ansatz求解的猜想是一致的。
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英文标题：
《The matrix product ansatz for the six-vertex model》
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作者：
Matheus Jatkoske Lazo
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最新提交年份：
2007
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分类信息：
一级分类：Physics 物理学
二级分类：Statistical Mechanics 统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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一级分类：Physics 物理学
二级分类：Strongly Correlated Electrons 强关联电子
分类描述：Quantum magnetism, non-Fermi liquids, spin liquids, quantum criticality, charge density waves, metal-insulator transitions
量子磁学，非费米液体，自旋液体，量子临界性，电荷密度波，金属-绝缘体跃迁
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英文摘要：
Recently it was shown that the eigenfunctions for the the asymmetric exclusion problem and several of its generalizations as well as a huge family of quantum chains, like the anisotropic Heisenberg model, Fateev- Zamolodchikov model, Izergin-Korepin model, Sutherland model, t-J model, Hubbard model, etc, can be expressed by a matrix product ansatz. Differently from the coordinate Bethe ansatz, where the eigenvalues and eigenvectors are plane wave combinations, in this ansatz the components of the eigenfunctions are obtained through the algebraic properties of properly defined matrices. In this work, we introduce a formulation of a matrix product ansatz for the six-vertex model with periodic boundary condition, which is the paradigmatic example of integrability in two dimensions. Remarkably, our studies of the six-vertex model are in agreement with the conjecture that all models exactly solved by the Bethe ansatz can also be solved by an appropriated matrix product ansatz.
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PDF链接：
https://arxiv.org/pdf/705.2044
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