Truncation identities for the small polaron fusion hierarchy
Truncation identities for the small polaron fusion hierarchy
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DOI：
10.1088/1367-2630/15/4/043026
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发表时间：
2012-11
影响因子：
3.3
通讯作者：
Andr'e M. Grabinski;H. Frahm
中科院分区：
文献类型：
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作者：
Andr'e M. Grabinski;H. Frahm
我们研究了相互作用的无自旋费米子的一维晶格模型。该模型对于周期性和开边界条件都是可积的;后者包括格拉斯曼值非对角边界场的存在，打破了模型的体积U（1）对称性。从嵌入到分次Yang-Baxter代数，该模型的可交换转移矩阵的一个无限的层次构造的融合过程。对于某些值的耦合常数相关的各向异性的基础顶点模型采取的根单位，这个层次被证明截断给出一个有限的一组函数方程的频谱的传输矩阵。对于一般的耦合常数，频谱问题是制定在一个功能（或TQ-）方程，可以解决周期性和对角开边界条件的Bethe anomaly方法。一般非对角边界场的模型的解决方案的可能途径进行了讨论。
We study a one-dimensional lattice model of interacting spinless fermions. This model is integrable for both periodic and open boundary conditions; the latter case includes the presence of Grassmann valued non-diagonal boundary fields breaking the bulk U(1) symmetry of the model. Starting from the embedding of this model into a graded Yang–Baxter algebra, an infinite hierarchy of commuting transfer matrices is constructed by means of a fusion procedure. For certain values of the coupling constant related to anisotropies of the underlying vertex model taken at roots of unity, this hierarchy is shown to truncate giving a finite set of functional equations for the spectrum of the transfer matrices. For generic coupling constants, the spectral problem is formulated in terms of a functional (or TQ-)equation which can be solved by Bethe ansatz methods for periodic and diagonal open boundary conditions. Possible approaches for the solution of the model with generic non-diagonal boundary fields are discussed.