In this paper, we use entangled states to construct 9 × 9-matrix representations of Temperley-Lieb algebra （TLA ）, then a family of 9 × 9-matrix representations of Birman-Wenzl-Murakami algebra （t3 WMA ）...In this paper, we use entangled states to construct 9 × 9-matrix representations of Temperley-Lieb algebra （TLA ）, then a family of 9 × 9-matrix representations of Birman-Wenzl-Murakami algebra （t3 WMA ） have been presented. Based on which, three topological basis states have been found. And we apply topological basis states to recast ninedimensional BWMA into its three-dimensional counterpart. Finally, we find the topological basis states are spin singlet states in special ease.展开更多
基金Supported by National Natural Science Foundation of China under Grant No. 10875026
文摘In this paper, we use entangled states to construct 9 × 9-matrix representations of Temperley-Lieb algebra （TLA ）, then a family of 9 × 9-matrix representations of Birman-Wenzl-Murakami algebra （t3 WMA ） have been presented. Based on which, three topological basis states have been found. And we apply topological basis states to recast ninedimensional BWMA into its three-dimensional counterpart. Finally, we find the topological basis states are spin singlet states in special ease.
