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The q-deformed Haldane-Shastry Spin Chain Model and the Corresponding Topological Basis Realization

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Abstract

In this paper, we show a q-deformed spin\(-\frac {1}{2}\) Haldane-Shastry (HS) chain with the symmetry of quantum group algebra, and find that the Hamiltonian of the system can be constructed from the Temperley-Lieb (TL) algebra generator. Based on this, it is shown that the topological basis states are the two eigenstaes of the four-qubit q-deformed spin\(-\frac {1}{2}\) HS chain. Specifically, the spin singlet states of the system all fall on the topological basis states. And the number of the spin singlet states of the system is equal to the number of the topological basis states. Meanwhile, in the case of antiferromagnetism, the energy ground state of the system falls on the topological subspace.

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Acknowledgments

This work was supported by the NSF of China (Grant No. 11575042), Natural Science Foundation of Jilin Province of China (Grant Nos. JJKH20190276KJ and JJKH20190279KJ) and the Fundamental Research Funds for the Central Universities (Grant No. 2412019FZ040).

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Authors and Affiliations

  1. Center for Quantum Sciences and School of Physics, Northeast Normal University, Changchun, 130024, China

    Yizi Zhu, Yue Deng & Chunfang Sun

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  1. Yizi Zhu
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  2. Yue Deng
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  3. Chunfang Sun
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Correspondence to Chunfang Sun.

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Zhu, Y., Deng, Y. & Sun, C. The q-deformed Haldane-Shastry Spin Chain Model and the Corresponding Topological Basis Realization. Int J Theor Phys 60, 4112–4121 (2021). https://doi.org/10.1007/s10773-021-04961-3

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