Functional Bethe ansatz methods for the open XXX chain
Functional Bethe ansatz methods for the open XXX chain
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DOI：
10.1088/1751-8113/44/1/015001
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发表时间：
2010-09
期刊：
影响因子：
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通讯作者：
H. Frahm;J. H. Grelik;A. Seel;T. Wirth
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文献类型：
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作者：
H. Frahm;J. H. Grelik;A. Seel;T. Wirth
研究了可积开XXX海森堡自旋链在非对角边界磁场作用下的谱。该模型的谱问题可以用分离变量得到的函数方程来表示，或者等价地用传递矩阵的融合来表示。对于一般的边界条件，特征值不能从许多代数Bethe方程的解中得到。基于仔细的有限大小的分析性质的底层层次的传递矩阵的研究，我们设计了两种方法来分析的功能方程。首先，我们介绍了一种截断方法，导致贝特型方程确定的自旋链的能谱。在第二种方法中，将函数方程的层次映射到TBA型非线性积分方程的无限系统。这两种方案具有互补的适用范围，便于对各种边界参数进行有效的数值分析。给出了在平行边界场限制下，对反铁磁基态能量的有限尺寸修正。
We study the spectrum of the integrable open XXX Heisenberg spin chain subject to non-diagonal boundary magnetic fields. The spectral problem for this model can be formulated in terms of functional equations obtained by separation of variables or, equivalently, from the fusion of transfer matrices. For generic boundary conditions the eigenvalues cannot be obtained from the solution of finitely many algebraic Bethe equations. Based on careful finite size studies of the analytic properties of the underlying hierarchy of transfer matrices we devise two approaches to analyze the functional equations. First we introduce a truncation method leading to Bethe-type equations determining the energy spectrum of the spin chain. In a second approach, the hierarchy of functional equations is mapped to an infinite system of nonlinear integral equations of TBA type. The two schemes have complementary ranges of applicability and facilitate an efficient numerical analysis for a wide range of boundary parameters. Some data are presented on the finite-size corrections to the energy of the state which evolves into the antiferromagnetic ground state in the limit of parallel boundary fields.