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Topological crystalline states are short-range entangled states jointly protected by onsite and crystalline symmetries.
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Chong Wang and T. Senthil, “Boson topological insulators: A window into highly entangled quantum phases,” Phys. Rev. B 87
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Xie Chen, Yuan-Ming Lu, and Ashvin Vishwanath, “Symmetry-protected topological phases from decorated domain walls,” Nature Communications 5
2014
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F. J. Burnell, Xie Chen, Lukasz Fidkowski, and Ashvin Vishwanath, “Exactly soluble model of a three-dimensional symmetry-protected topological phase of bosons with surface topological order,” Phys. Rev. B 90
2014
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Zheng-Cheng Gu and Xiao-Gang Wen, “Symmetry-protected topological orders for interacting fermions: Fermionic topological nonlinear σ \sigma models and a special group supercohomology theory,” Phys. Rev. B 90
2014
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Ken Shiozaki and Masatoshi Sato, “Topology of crystalline insulators and superconductors,” Phys. Rev. B 90
2014
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Xiao-Gang Wen, “Construction of bosonic symmetry-protected-trivial states and their topological invariants via G × S O ( ∞ ) G\times{}SO(\infty) nonlinear σ \sigma models,” Phys. Rev. B 91
2015
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Anton Kapustin, Ryan Thorngren, Alex Turzillo, and Zitao Wang, “Fermionic symmetry protected topological phases and cobordisms,” Journal of High Energy Physics 2015
2015
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Hiroki Isobe and Liang Fu, “Theory of interacting topological crystalline insulators,” Phys. Rev. B 92
2015
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2017
Later among the works it cites.
Qing-Rui Wang and Zheng-Cheng Gu, “Towards a complete classification of symmetry-protected topological phases for interacting fermions in three dimensions and a general group supercohomology theory,” Phys. Rev. X 8
2018
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Juven Wang, Kantaro Ohmori, Pavel Putrov, Yunqin Zheng, Zheyan Wan, Meng Guo, Hai Lin, Peng Gao, and Shing-Tung Yau, “Tunneling topological vacua via extended operators: (Spin-)TQFT spectra and boundary deconfinement in various dimensions,” Prog. Theor. Exp. Phys. 2018
2018
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Zhida Song, Tiantian Zhang, Zhong Fang, and Chen Fang, “Quantitative mappings between symmetry and topology in solids,” Nature Communications 9
2018
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Eslam Khalaf, Hoi Chun Po, Ashvin Vishwanath, and Haruki Watanabe, “Symmetry indicators and anomalous surface states of topological crystalline insulators,” Phys. Rev. X 8
2018
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2018
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Ryan Thorngren and Dominic V. Else, “Gauging spatial symmetries and the classification of topological crystalline phases,” Phys. Rev. X 8
2018
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Xu Yang, Shenghan Jiang, Ashvin Vishwanath, and Ying Ran, “Dyonic lieb-schultz-mattis theorem and symmetry protected topological phases in decorated dimer models,” Phys. Rev. B 98
2018
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Tian Lan, Chenchang Zhu, and Xiao-Gang Wen, “Fermion decoration construction of symmetry-protected trivial order for fermion systems with any symmetry and in any dimension,” Phys. Rev. B 100
2019
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Zhida Song, Sheng-Jie Huang, Yang Qi, Chen Fang, and Michael Hermele, “Topological states from topological crystals,” Science Advances 5
2019
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Alex Turzillo and Minyoung You, “Fermionic matrix product states and one-dimensional short-range entangled phases with antiunitary symmetries,” Phys. Rev. B 99
2019
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Dominic V. Else and Ryan Thorngren, “Crystalline topological phases as defect networks,” Phys. Rev. B 99
2019
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Yuan-Ming Lu, Ying Ran, and Masaki Oshikawa, “Filling-enforced constraint on the quantized hall conductivity on a periodic lattice,” Annals of Physics 413
2020
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Dominic V. Else and Ryan Thorngren, “Topological theory of lieb-schultz-mattis theorems in quantum spin systems,” Phys. Rev. B 101
2020
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Alex Rasmussen and Yuan-Ming Lu, “Classification and construction of higher-order symmetry-protected topological phases of interacting bosons,” Phys. Rev. B 101
2020
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