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Chin. Phys. B, 2012, Vol. 21(2): 020305    DOI: 10.1088/1674-1056/21/2/020305
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A 9×9 matrix representation of Temperley–Lieb algebra and corresponding entanglement

Gou Li-Dan(苟立丹) and Zhu Rui-Han(朱瑞晗)
School of Science, Changchun University of Science and Technology, Changchun 130022, China
Abstract  We present the matrix U. The $9\times9$ U matrix is a representation of specialized Temperley-Lieb algebra. Based on which, a unitary $\check{R}$ matrix is generated via the Yang-Baxterization approach. The  $9\times9$$\check{R}$  matrix, a solution of the Yang-Baxter equation, is universal for quantum entanglement.
Keywords:  Temperley-Lieb algebra      Yang-Baxter equation      entanglement  
Received:  17 April 2011      Revised:  09 November 2011      Accepted manuscript online: 
PACS:  03.67.Mn (Entanglement measures, witnesses, and other characterizations)  
  03.65.Fd (Algebraic methods)  
  02.20.-a (Group theory)  
Fund: Project supported by the Science Foundation of the Education Department of Jilin Province, China (Grant No. 2011JTY11).
Corresponding Authors:  Gou Li-Dan,gouly@sina.com     E-mail:  gouly@sina.com

Cite this article: 

Gou Li-Dan(苟立丹) and Zhu Rui-Han(朱瑞晗) A 9×9 matrix representation of Temperley–Lieb algebra and corresponding entanglement 2012 Chin. Phys. B 21 020305

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