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Topological Basis Method for Four-Qubit Spin-\(\frac {1}{2}\) XXZ Heisenberg Chain with Dzyaloshinskii-Moriya Interaction

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Abstract

In this paper, we investigate the four-qubit spin-\(\frac {1}{2}\) XXZ Heisenberg chain with Dzyaloshinskii-Moriya interaction by topological basis method, and research the relationship between the topological basis states and the ground states. In order to study the Hamiltonian system beyond XXZ model, we introduce two Temperley-Lieb algebra generators and two other generalized generators. Then we investigate the relationship between topological basis and Heisenberg XXZ model with Dzyaloshinskii-Moriya interaction. The results show that the ground state of this model falls on the topological basis state for anti-ferromagnetic case and gapless phase case.

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Authors and Affiliations

  1. Changchun Normal University, Changchun, Jilin, 130000, People’s Republic of China

    Bo Liu

  2. Northeast Normal University, Changchun, Jilin, 130000, People’s Republic of China

    Kang Xue & Gangcheng Wang

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  1. Bo Liu
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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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Liu, B., Xue, K. & Wang, G. Topological Basis Method for Four-Qubit Spin-\(\frac {1}{2}\) XXZ Heisenberg Chain with Dzyaloshinskii-Moriya Interaction. Int J Theor Phys 56, 802–809 (2017). https://doi.org/10.1007/s10773-016-3223-4

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  • DOI: https://doi.org/10.1007/s10773-016-3223-4

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