可积$gl_{\mathcal{M}|\mathcal{N}}$和哈伯德模型的分离变量基
Separation of variables bases for integrable $gl_{\mathcal{M}|\mathcal{N}}$ and Hubbard models
摘要：
我们构造了基本非齐次$gl_{\mathcal{M}|\mathcal{N}}$超对称可积模型和非齐次哈伯德模型的量子变量分离基. SoV基是通过使用这些量子模型的可积结构获得的，即相关的交换转移矩阵，遵循[1]中介绍的一般方案;即，它们由转移矩阵对一般共向量的多重作用产生的状态集给出。这类SoV基的存在性意味着相应的转移矩阵具有非退化谱，并且如果定义拟周期边界条件的扭矩阵具有简单谱可对角化的性质，则相应的转移矩阵具有简单谱可对角化的性质.此外，在这些SoV基地的传递矩阵特征值问题的决议导致的解决方案的全谱问题，即本征值和本征向量。事实上，任何特征值都与唯一的（直到平凡的整体归一化）特征向量相关联，其在SoV基中的波函数被分解为在单独变量的谱上计算的相应传递矩阵特征值的乘积。作为一个应用，我们在我们的SoV框架下的基本$gl_{1|2}$超对称可积模型与一类特殊的扭曲矩阵的传输矩阵谱完全表征。从这些结果中，我们也证明了这种情况下的Bethe Anglands的完整性。基本非齐次$gl_{\mathcal{M}|\mathcal{N}}$超对称可积模型和一般扭曲边界条件下的非齐次哈伯德模型的谱问题的完整解将在未来的出版物中讨论。
英文摘要：
We construct quantum Separation of Variables (SoV) bases for both the fundamental inhomogeneous $gl_{\mathcal{M}|\mathcal{N}}$ supersymmetric integrable models and for the inhomogeneous Hubbard model both defined with quasi-periodic twisted boundary conditions given by twist matrices having simple spectrum. The SoV bases are obtained by using the integrable structure of these quantum models,i.e. the associated commuting transfer matrices, following the general scheme introduced in [1]; namely, they are given by set of states generated by the multiple action of the transfer matrices on a generic co-vector. The existence of such SoV bases implies that the corresponding transfer matrices have non degenerate spectrum and that they are diagonalizable with simple spectrum if the twist matrices defining the quasi-periodic boundary conditions have that property. Moreover, in these SoV bases the resolution of the transfer matrix eigenvalue problem leads to the resolution of the full spectral problem, i.e. both eigenvalues and eigenvectors. Indeed, to any eigenvalue is associated the unique (up to a trivial overall normalization) eigenvector whose wave-function in the SoV bases is factorized into products of the corresponding transfer matrix eigenvalue computed on the spectrum of the separate variables. As an application, we characterize completely the transfer matrix spectrum in our SoV framework for the fundamental $gl_{1|2}$ supersymmetric integrable model associated to a special class of twist matrices. From these results we also prove the completeness of the Bethe Ansatz for that case. The complete solution of the spectral problem for fundamental inhomogeneous $gl_{\mathcal{M}|\mathcal{N}}$ supersymmetric integrable models and for the inhomogeneous Hubbard model under the general twisted boundary conditions will be addressed in a future publication.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
