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The quantum spin chains of Temperley–Lieb type and the topological basis states

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Abstract

In this paper, based on the usual spin basis, we present a complete orthonormal basis with the single loop \(d=\sqrt{2}\) consisting of maximally entangled four-qubit states. Then we investigate the particular physical properties of the topological basis states in the corresponding quantum spin chains of Temperley–Lieb type. Whether the system is the anti-ferromagnetic case or the ferromagnetic case, the ground states are all doubly degenerate, and they all fall on the topological basis states. Furthermore, we introduce the Yangian \(Y(sl(2))\) operators to investigate the transitions between the quantum states.

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Acknowledgments

This work was supported by NSF of China (grants No. 11175043 and No. 11205028) and the Fundamental Research Funds for the Central Universities (Grants No. 11QNJJ010 and No. 11SSXT147).

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Authors and Affiliations

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

    Chunfang Sun, Kang Xue, Gangcheng Wang, Chengcheng Zhou & Guijiao Du

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  1. Chunfang Sun
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  2. Kang Xue
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  3. Gangcheng Wang
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Correspondence to Kang Xue.

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Sun, C., Xue, K., Wang, G. et al. The quantum spin chains of Temperley–Lieb type and the topological basis states. Quantum Inf Process 12, 3079–3092 (2013). https://doi.org/10.1007/s11128-013-0542-8

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