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Quantum Information Processing
Published in: Quantum Information Processing 2/2014

01-02-2014

The topological basis expression of Heisenberg spin chain

Authors: Taotao Hu, Hang Ren, Kang Xue

Published in: Quantum Information Processing | Issue 2/2014

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Abstract

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.
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Metadata
Title
The topological basis expression of Heisenberg spin chain
Authors
Taotao Hu
Hang Ren
Kang Xue
Publication date
01-02-2014
Publisher
Springer US
Published in
Quantum Information Processing / Issue 2/2014
Print ISSN: 1570-0755
Electronic ISSN: 1573-1332
DOI
https://doi.org/10.1007/s11128-013-0658-x

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