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24 April 2024

» arxiv » 0904.0090

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Approach of constructing Temperley-Lieb algebras representation and entanglement in a new Yang-Baxter system
Chunfang Sun ; Gangcheng Wang ; Taotao Hu ; Chengcheng Zhou ; Qingyong Wang ; Kang Xue ;
Date:	1 Apr 2009
Abstract:	A more general reducible representation of the Temperley-Lieb algebra (TLA) is constructed on the tensor product of $n$-dimensional spaces. Specifically, it is shown that via a combination approach, one can construct some more significant $n^{2} imes n^{2}$ matrices $U$ which satisfy the TLA. Then we present a $9 imes9$ matrix $U$ with the single loop $d=sqrt{3}$. Via Yang-Baxterization approach, we obtain a unitary $ reve{R}( heta ,varphi_{1},varphi_{2})$-matrix, a solution of the Yang-Baxter Equation. The entanglement properties of $reve{R}$-matrix is investigated, and the arbitrary degree of entanglement for two-qutrit entangled states can be generated when $reve{R}$-matrix acts on the standard basis(separable states).
Source:	arXiv, 0904.0090
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