论文标题
一个耦合的templeley-lieb代数，用于整合性手性potts链
A coupled Temperley-Lieb algebra for the superintegrable chiral Potts chain
论文作者
论文摘要
$ n $ n $ state可促进性手性波特（SICP）模型的哈密顿量是根据由$ N-1 $类型的templeley-lieb发电机定义的耦合代数编写的。这将概括为$ n = 3 $的先前结果，由J. F. Fjelstad和T.Månsson[J. J.物理。 a {\ bf 45}（2012）155208]。 $ n = 3 $案例给出了相关耦合代数的图形表示，该案例涉及对templeley-lieb代数的绘画演示的概括，其中包括一个围绕循环纠缠的极点。对于该代数的两个已知表示形式，$ n = 3 $ SICP链和交错的自旋1/2 XX链，封闭（合同）循环具有重量$ \ sqrt {3} $和权重$ 2 $。对于两种表示，在杆周围封闭（不可汇总）环的重量为零。图形表示提供了代数关系的图形解释。分辨率分辨率的关键要素是环绕杆的环关系的一个交叉关系，涉及SICP链的参数$ρ= e^{2π\ Mathrm {i}/3} $，而$ρ= 1 $对于错位xx链。假设Kauffman支架旋转关系，这些$ρ$值是派生的。
The hamiltonian of the $N$-state superintegrable chiral Potts (SICP) model is written in terms of a coupled algebra defined by $N-1$ types of Temperley-Lieb generators. This generalises a previous result for $N=3$ obtained by J. F. Fjelstad and T. Månsson [J. Phys. A {\bf 45} (2012) 155208]. A pictorial representation of a related coupled algebra is given for the $N=3$ case which involves a generalisation of the pictorial presentation of the Temperley-Lieb algebra to include a pole around which loops can become entangled. For the two known representations of this algebra, the $N=3$ SICP chain and the staggered spin-1/2 XX chain, closed (contractible) loops have weight $\sqrt{3}$ and weight $2$, respectively. For both representations closed (non-contractible) loops around the pole have weight zero. The pictorial representation provides a graphical interpretation of the algebraic relations. A key ingredient in the resolution of diagrams is a crossing relation for loops encircling a pole which involves the parameter $ρ= e^{ 2π\mathrm{i}/3}$ for the SICP chain and $ρ=1$ for the staggered XX chain. These $ρ$ values are derived assuming the Kauffman bracket skein relation.
