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Exact solution to a class of generalized Kitaev spin-1/2 models in arbitrary dimensions

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Abstract

We construct a class of exactly solvable generalized Kitaev spin-1/2 models in arbitrary dimensions, which is beyond the category of quantum compass models. The Jordan-Wigner transformation is employed to prove the exact solvability. An exactly solvable quantum spin-1/2 model can be mapped to a gas of free Majorana fermions coupled to static Z2 gauge fields. We classify these exactly solvable models according to their parent models. Any model belonging to this class can be generated by one of the parent models. For illustration, a two dimensional (2D) tetragon-octagon model and a three dimensional (3D) xy bond model are studied.

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Authors and Affiliations

  1. Kavli Institute for Theoretical Sciences, University of Chinese Academy of Sciences, Beijing, 100190, China

    JianJian Miao & FuChun Zhang

  2. Department of Physics, Zhejiang University, Hangzhou, 310027, China

    HuiKe Jin & Yi Zhou

  3. CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing, 100190, China

    FuChun Zhang & Yi Zhou

  4. Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing, 210093, China

    FuChun Zhang & Yi Zhou

  5. Beijing National Laboratory for Condensed Matter Physics & Institute of Physics, Chinese Academy of Sciences, Beijing, 100190, China

    Yi Zhou

Authors
  1. JianJian Miao
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  2. HuiKe Jin
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  3. FuChun Zhang
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  4. Yi Zhou
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Corresponding author

Correspondence to Yi Zhou.

Additional information

JianJian Miao is supported by the China Postdoctoral Science Foundation of China (Grant No. 2017M620880), and the National Natural Science Foundation of China (Grant No. 1184700424). Yi Zhou is supported by the National Key Research and Development Program of China (Grant No. 2016YFA0300202), the National Basic Research Program of China (Grant No. 2014CB921201), the National Natural Science Foundation of China (Grant No. 11774306), the Key Research Program of the Chinese Academy of Sciences (Grant No. XDPB08-4), and the Fundamental Research Funds for the Central Universities in China. FuChun Zhang is supported by the National Natural Science Foundation of China (Grant No. 11674278), the National Basic Research Program of China (Grant No. 2014CB921203), and the CAS Center for Excellence in Topological Quantum Computation.

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Miao, J., Jin, H., Zhang, F. et al. Exact solution to a class of generalized Kitaev spin-1/2 models in arbitrary dimensions. Sci. China Phys. Mech. Astron. 63, 247011 (2020). https://doi.org/10.1007/s11433-019-1442-2

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  • DOI: https://doi.org/10.1007/s11433-019-1442-2

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