Temperley-Lieb Algebra, Yang-Baxterization and Universal Gate

Abstract

A method of constructing $n^2\times n^2$ matrix solutions(with $n^3$ matrix elements) of Temperley-Lieb algebra relation is presented in this paper. The single loop of these solutions are $d=\sqrt{n}$. Especially, a $9\times 9-$matrix solution with single loop d=$\sqrt{3}$ is discussed in detail. An unitary Yang-Baxter $\breve{R}(\theta ,q_1,q_2)$ matrix is obtained via the Yang-Baxterization process. The entanglement property and geometric property (\emph{i.e.} Berry Phase) of this Yang-Baxter system are explored.

12 pages

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Cited by in corpus (8)

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• Temperley-Lieb R-matrices from generalized Hadamard matrices
• Tensor space representations of Temperley-Lieb algebra via orthogonal projections of rank $r\ge 1$
• Birman-Wenzl-Murakami Algebra and the Topological Basis
• Tensor space representations of Temperley-Lieb algebra and generalized permutation matrices
• Reflection matrices from Hadamard-type Temperley-Lieb R-matrices
• Birman-Wenzl-Murakami Algebra, Topological parameter and Berry phase