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Phase Transition of the q-State Clock Model: Duality and Tensor Renormalization |
| Jing Chen1,2, Hai-Jun Liao1**, Hai-Dong Xie1,2, Xing-Jie Han1,2, Rui-Zhen Huang1,2, Song Cheng1,2, Zhong-Chao Wei3, Zhi-Yuan Xie4,1, Tao Xiang1,2,5** |
1Institute of Physics, Chinese Academy of Sciences, P. O. Box 603, Beijing 100190
2University of Chinese Academy of Sciences, Beijing 100049
3Institute for Theoretical Physics, University of Cologne, Cologne 50937, Germany
4Department of Physics, Renmin University of China, Beijing 100872
5Collaborative Innovation Center of Quantum Matter, Beijing 100190
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| Cite this article: |
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Jing Chen, Hai-Jun Liao, Hai-Dong Xie et al 2017 Chin. Phys. Lett. 34 050503 |
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Abstract We investigate the critical behavior and the duality property of the ferromagnetic $q$-state clock model on the square lattice based on the tensor-network formalism. From the entanglement spectra of local tensors defined in the original and dual lattices, we obtain the exact self-dual points for the model with $q \leq 5 $ and approximate self-dual points for $q \geq 6$. We calculate accurately the lower and upper critical temperatures for the six-state clock model from the fixed-point tensors determined using the higher-order tensor renormalization group method and compare with other numerical results.
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Received: 24 April 2017
Published: 29 April 2017
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| Fund: Supported by the National Natural Science Foundation of China under Grant No 11474331. |
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