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19 April 2024

» arxiv » 0903.3711

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Temperley-Lieb Algebra, Yang-Baxterization and Universal Gate
Gangcheng Wang ; Chengcheng Zhou ; Chunfang Sun ; Qingyong Wang ; Kang Xue ;
Date:	23 Mar 2009
Abstract:	A method for constructing $n^{2} imes n^{2}$ matrix representation (with $n^{3}$ matrix elements) of Temperley-Lieb algebra(TLA) is presented in this paper. The single loop of these representation are $d=sqrt{n}$. Especially, a $9 imes9-$ matrix representation with single loop d=$sqrt{3}$ is discussed in detail. An unitary Yang-Baxter $reve{R}( heta,q_{1},q_{2})$ matrix is obtained by the Yang-Baxterization process. The entanglement property and geometric property (emph{i.e.} Berry Phase) are explored.
Source:	arXiv, 0903.3711
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