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Birman–Wenzl–Murakami algebra, topological parameter and Berry phase

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Abstract

In this paper, a 3 × 3-matrix representation of Birman–Wenzl–Murakami (BWM) algebra has been presented. Based on which, unitary matrices A(θ, φ 1, φ 2) and B(θ, φ 1, φ 2) are generated via Yang–Baxterization approach. A Hamiltonian is constructed from the unitary B(θ, φ) matrix. Then we study Berry phase of the Yang–Baxter system, and obtain the relationship between topological parameter and Berry phase.

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Authors and Affiliations

  1. School of Physics, Northeast Normal University, Changchun, 130024, People’s Republic of China

    Chengcheng Zhou, Kang Xue, Lidan Gou, Chunfang Sun, Gangcheng Wang & Taotao Hu

  2. School of Science, Changchun University of Science and Technology, Changchun, 130022, People’s Republic of China

    Lidan Gou

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  1. Chengcheng Zhou
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  2. Kang Xue
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  3. Lidan Gou
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  4. Chunfang Sun
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Correspondence to Kang Xue.

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Zhou, C., Xue, K., Gou, L. et al. Birman–Wenzl–Murakami algebra, topological parameter and Berry phase. Quantum Inf Process 11, 1765–1773 (2012). https://doi.org/10.1007/s11128-011-0331-1

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