Phase Transition of the q-State Clock Model： Duality and Tensor Renormalization

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 m...

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Published inChinese physics letters Vol. 34; no. 5; pp. 27 - 30
Main Author 陈靖 廖海军 谢海东 韩兴杰 黄瑞珍 程嵩 魏忠超 谢志远 向涛
Format Journal Article
LanguageEnglish
Published 01.05.2017
Subjects
临界温度
对偶性
张量
时钟
模型基
相变
自对偶点
重整化群方法
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ISSN0256-307X
1741-3540
DOI10.1088/0256-307X/34/5/050503

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Summary: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 ≤ 5 and approximate self-dual points for q ≥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.
Bibliography:11-1959/O4
Jing Chen1,2, Hai-Jun Liao1, Hai-Dong Xie1,2, Xing-Jie Han1,2, Rui-Zhen Huang,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 ; 2 University 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）
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 ≤ 5 and approximate self-dual points for q ≥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.
ISSN:0256-307X
1741-3540
DOI:10.1088/0256-307X/34/5/050503