Temperley-Lieb (T-L) algebra plays an important role in quantum computation, quantum teleportation, knot theory, statistical physics and topological quantum field theory. At the same time, a large number of models are represented by the generators of T-L algebra. In this paper, it is shown that the XY model can be constructed from the linear combination of the T-L algebra generators.We construct three new topological basis states, then investigate the particular properties of the topological basis in this system. For instance the energy ground state of the system falls on one of the topological basis states.

中文翻译：

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XY自旋链和拓扑基础实现

Temperley-Lieb (TL) 代数在量子计算、量子隐形传态、结理论、统计物理学和拓扑量子场论中发挥着重要作用。同时，大量的模型以TL代数的生成器为代表。在本文中，表明可以从TL代数发生器的线性组合构建XY模型。我们构建了三个新的拓扑基态，然后研究了该系统中拓扑基的特殊性质。例如，系统的能量基态落在拓扑基态之一。