Integrable boundary conditions for the one-dimensional Hubbard model
Integrable boundary conditions for the one-dimensional Hubbard model
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DOI：
10.1143/jpsj.66.2288
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发表时间：
1997-08
影响因子：
1.7
通讯作者：
M. Shiroishi;M. Wadati
中科院分区：
文献类型：
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作者：
M. Shiroishi;M. Wadati
在量子逆散射方法(QISM)框架下讨论了一维Hubbard模型的可积边界条件。我们使用Olmedilla等人提出的费米子R-矩阵。处理扭曲周期边界条件和开边界条件。通过考虑费米子R-矩阵的对称矩阵，我们确定了可积扭曲周期边界条件的最一般形式。为了求可积开边界条件，我们求解梯度反射方程，得到两个对角解，分别对应于a)边界化学势和b)边界磁场。利用费米子R矩阵的对称矩阵和梯度反射方程的协方差性质，得到了非对角解。它们可以解释为对角解的S O(4)旋转。
We discuss the integrable boundary conditions for the one-dimensional (1D) Hubbard Model in the framework of the Quantum Inverse Scattering Method (QISM). We use the fermionic R -matrix proposed by Olmedilla et al. to treat the twisted periodic boundary condition and the open boundary condition. We determine the most general form of the integrable twisted periodic boundary condition by considering the symmetry matrix of the fermionic R -matrix. To find the integrable open boundary condition, we shall solve the graded reflection equation, and find there are two diagonal solutions, which correspond to a) the boundary chemical potential and b) the boundary magnetic field. Non-diagonal solutions are obtained using the symmetry matrix of the fermionic R -matrix and the covariance property of the graded reflection equation. They can be interpreted as the S O (4) rotations of the diagonal solutions.