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We build exactly solvable lattice Hamiltonians for fermionic symmetry-protected topological (SPT) phases in (3+1)D classified by group supercohomology.
1912
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1947
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Richard Z Goldstein and Edward C Turner, “A formula for stiefel-whitney homology classes,” Proceedings of the American Mathematical Society 58
1976
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Robbert Dijkgraaf and Edward Witten, “Topological Gauge Theories and Group Cohomology,” Commun. Math. Phys. 129
1990
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Michael Levin and Xiao-Gang Wen, “Fermions, strings, and gauge fields in lattice spin models,” Phys. Rev. B 67
2003
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Andreas P Schnyder, Shinsei Ryu, Akira Furusaki, and Andreas WW Ludwig, “Classification of topological insulators and superconductors in three spatial dimensions,” Physical Review B 78
2008
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Alexei Kitaev, “Periodic table for topological insulators and superconductors,” in AIP conference proceedings , Vol. 1134 (American Institute of Physics, 2009) pp. 22–30
2009
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Xie Chen, Zheng-Cheng Gu, and Xiao-Gang Wen, “Local unitary transformation, long-range quantum entanglement, wave function renormalization, and topological order,” Phys. Rev. B 82
2010
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Shinsei Ryu, Andreas P Schnyder, Akira Furusaki, and Andreas WW Ludwig, “Topological insulators and superconductors: tenfold way and dimensional hierarchy,” New Journal of Physics 12
2010
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Arijeet Pal and David A. Huse, “Many-body localization phase transition,” Phys. Rev. B
2010
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Michael Levin and Zheng-Cheng Gu, “Braiding statistics approach to symmetry-protected topological phases,” Phys. Rev. B 86
2012
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Xie Chen, Zheng-Cheng Gu, Zheng-Xin Liu, and Xiao-Gang Wen, “Symmetry protected topological orders and the group cohomology of their symmetry group,” Phys. Rev. B 87
2013
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David A. Huse, Rahul Nandkishore, Vadim Oganesyan, Arijeet Pal, and S. L. Sondhi, “Localization-protected quantum order,” Phys. Rev. B
2013
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Bela Bauer and Chetan Nayak, “Area laws in a many-body localized state and its implications for topological order,” Journal of Statistical Mechanics: Theory and Experiment 2013
2013
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Lukasz Fidkowski, Xie Chen, and Ashvin Vishwanath, “Non-abelian topological order on the surface of a 3d topological superconductor from an exactly solved model,” Phys. Rev. X 3
2013
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2014
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Dominic V. Else and Chetan Nayak, “Classifying symmetry-protected topological phases through the anomalous action of the symmetry on the edge,” 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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Anushya Chandran, Vedika Khemani, C. R. Laumann, and S. L. Sondhi, “Many-body localization and symmetry-protected topological order,” Phys. Rev. B
2014
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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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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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Chenjie Wang and Michael Levin, “Topological invariants for gauge theories and symmetry-protected topological phases,” Phys. Rev. B 91
2015
Cited alongside, same era.
2015
Cited alongside, same era.
Yasaman Bahri, Ronen Vosk, Ehud Altman, and Ashvin Vishwanath, “Localization and topology protected quantum coherence at the edge of hot matter,” Nat. Commun. 6
2015
Cited alongside, same era.
Chenjie Wang, “Braiding statistics and classification of two-dimensional charge- 2 m 2m superconductors,” Phys. Rev. B 94
2016
Cited alongside, same era.
Beni Yoshida, “Topological phases with generalized global symmetries,” Phys. Rev. B 93
2016
2018
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2018
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2018
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Davide Gaiotto and Theo Johnson-Freyd, “Symmetry protected topological phases and generalized cohomology,” Journal of High Energy Physics 2019
2019
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Cited alongside, same era.
Chris Heinrich, Fiona Burnell, Lukasz Fidkowski, and Michael Levin, “Symmetry-enriched string nets: Exactly solvable models for set phases,” Phys. Rev. B 94
2016
Cited alongside, same era.
Andrew C. Potter and Romain Vasseur, “Symmetry constraints on many-body localization,” Phys. Rev. B 94
2016
Cited alongside, same era.
Nicolas Tarantino and Lukasz Fidkowski, “Discrete spin structures and commuting projector models for two-dimensional fermionic symmetry-protected topological phases,” Phys. Rev. B 94
2016
Cited alongside, same era.
Davide Gaiotto and Anton Kapustin, “Spin tqfts and fermionic phases of matter,” International Journal of Modern Physics A 31
2016
Cited alongside, same era.
Chenjie Wang, Chien-Hung Lin, and Zheng-Cheng Gu, “Interacting fermionic symmetry-protected topological phases in two dimensions,” Phys. Rev. B 95
2017
Cited alongside, same era.
Lukasz Fidkowski and Ashvin Vishwanath, “Realizing anomalous anyonic symmetries at the surfaces of three-dimensional gauge theories,” Phys. Rev. B 96
2017
Cited alongside, same era.
Anton Kapustin and Ryan Thorngren, “Fermionic spt phases in higher dimensions and bosonization,” Journal of High Energy Physics 2017
2017
Cited alongside, same era.
Yu-An Chen and Anton Kapustin, “Bosonization in three spatial dimensions and a 2-form gauge theory,” Phys. Rev. B 100
2019
Later among the works it cites.
Tyler D. Ellison and Lukasz Fidkowski, “Disentangling interacting symmetry-protected phases of fermions in two dimensions,” Phys. Rev. X 9
2019
Later among the works it cites.
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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Ryohei Kobayashi, Kantaro Ohmori, and Yuji Tachikawa, “On gapped boundaries for spt phases beyond group cohomology,” Journal of High Energy Physics 2019
2019
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David Aasen, Ethan Lake, and Kevin Walker, “Fermion condensation and super pivotal categories,” Journal of Mathematical Physics 60
2019
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Qing-Rui Wang, Yang Qi, and Zheng-Cheng Gu, “Anomalous Symmetry Protected Topological States in Interacting Fermion Systems,” Phys. Rev. Lett. 123
2019
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Jun Ho Son and Jason Alicea, “Commuting-projector hamiltonians for two-dimensional topological insulators: Edge physics and many-body invariants,” Phys. Rev. B 100
2019
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2019
Later among the works it cites.
Meng Cheng, “Fermionic lieb-schultz-mattis theorems and weak symmetry-protected phases,” Phys. Rev. B 99
2019
Later among the works it cites.
Meng Guo, Kantaro Ohmori, Pavel Putrov, Zheyan Wan, and Juven Wang, “Fermionic finite-group gauge theories and interacting symmetric/crystalline orders via cobordisms,” Communications in Mathematical Physics , 1–82 (2020)
2020
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Yu-An Chen, “Exact bosonization in arbitrary dimensions,” Phys. Rev. Research 2
2020
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Lokman Tsui and Xiao-Gang Wen, “Lattice models that realize ℤ n \mathbb{Z}_{n} -1 symmetry-protected topological states for even n n ,” Phys. Rev. B 101
2020
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2020
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Yuji Tachikawa, “On gauging finite subgroups,” SciPost Phys. 8
2020
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Qing-Rui Wang and Zheng-Cheng Gu, “Construction and classification of symmetry-protected topological phases in interacting fermion systems,” Phys. Rev. X 10
2020
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Ryohei Kobayashi, “Commuting projector models for ( 3 + 1 3+1 )-dimensional topological superconductors via a string net of ( 1 + 1 1+1 )-dimensional topological superconductors,” Phys. Rev. B 102
2020
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