The XY Spin Chain and the Topological Basis Realization

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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.