In this paper, it is shown that the Heisenberg XY, XXZ, XXX, and Ising model all can be constructed from the Braid group algebra generator and the Temperley–Lieb algebra generator. And a new set of topological basis expression is presented. Through acting on the different subspaces, we get the new nontrivial six-dimensional and four-dimensional Braid group matrix representations and Temperley–Lieb matrix representations. The eigenstates of Heisenberg model can be described by the combination of the set of topological bases. It is worth mentioning that the ground state is closely related to parameter q which is the meaningful topological parameter.
Quantum Information Processing – Springer Journals
Published: Nov 1, 2013
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