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We develop a mathematical theory of symmetry protected trivial (SPT) orders and anomaly-free symmetry enriched topological (SET) orders in all dimensions via two different approaches with an emphasis on the second approach.
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G. Carnovale, The Brauer group of modified supergroup algebras, J. Algebra 305 (2) (2006), 993-1036
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A. Davydov, D. Nikshych, Braided Picard groups and graded extensions of braided tensor categories
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S. Willerton, The twisted Drinfeld double of a finite group via gerbes and finite groupoids
2008
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Z.-C. Gu and X.-G. Wen, Tensor-Entanglement-Filtering Renormalization Approach and Symmetry Protected Topological Order , Phys. Rev. B 80
2009
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X. Chen, Z.-C. Gu, and X.-G. Wen, Local unitary transformation, long-range quantum entanglement, wave function renormalization, and topological order , Phys. Rev. B 82
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V. Drinfeld, S. Gelaki, D. Nikshych, V. Ostrik, On braided fusion categories
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P. Etingof, D. Nikshych, V. Ostrik, Fusion categories and homotopy theory
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Lukasz Fidkowski and Alexei Kitaev, Effects of interactions on the topological classification of free fermion systems
2010
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2011
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L. Fidkowski and A. Kitaev, Topological phases of fermions in one dimension
2011
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D. Gaiotto and A. Kapustin, Spin TQFTs and fermionic phases of matter , Int. J. Mod. Phys. A 31
2016
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T. Lan, L. Kong, and X.-G. Wen, Modular Extensions of Unitary Braided Fusion Categories and 2+1D Topological/SPT Orders with Symmetries , Commun. Math. Phys. 351
2016
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B. Swingle and J. McGreevy, Renormalization group constructions of topological quantum liquids and beyond , Phys. Rev. B 93
2016
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Y.H. Ai, L. Kong, H. Zheng, Topological orders and factorization homology
2017
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N. Schuch, D. Pérez-García, and I. Cirac, Classifying quantum phases using matrix product states and projected entangled pair states , Phys. Rev. B 84
2011
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A. Kitaev, L. Kong, Models for Gapped Boundaries and Domain Walls
2012
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X. Chen, Z.-C. Gu, Z.-X. Liu, and X.-G. Wen, Symmetry protected topological orders and the group cohomology of their symmetry group , Phys. Rev. B 87
2013
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2013
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A. Davydov, D. Nikshych, The Picard crossed module of a braided tensor category
2013
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A. Davydov, D. Nikshych, V. Ostrik, On the structure of the Witt group of braided fusion categories
2013
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M. Barkeshli, P. Bonderson, M. Cheng, and Z. Wang, Symmetry, Defects, and Gauging of Topological Phases (2014), a rXiv:1410.4540
2014
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P. Bruillard, C. Galindo, T. Hagge, S.-H. Ng, J.Y. Plavnik, E.C. Rowell, Z. Wang Fermionic modular categories and the 16-fold way
2017
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C. Galindo, C.F. Venegas-Ramírez, Categorical fermionic actions and minimal modular extensions
2017
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A. Kapustin and R. Thorngren, Fermionic SPT phases in higher dimensions and bosonization , J. High Energ. Phys. 2017
2017
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L. Kong, X.-G. Wen, H. Zheng, Boundary-bulk relation in topological orders
2017
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T. Lan, L. Kong, and X.-G. Wen, Classification of (2+1)-dimensional topological order and symmetry-protected topological order for bosonic and fermionic systems with on-site symmetries , Phys. Rev. B 95
2017
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C.L. Douglas, D.J. Reutter, Fusion 2-categories and a state-sum invariant for 4-manifolds
2018
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L. Kong, H. Zheng, The center functor is fully faithful
2018
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T. Lan, L. Kong, and X.-G. Wen, Classification of (3+1)D Bosonic Topological Orders: The Case When Pointlike Excitations Are All Bosons , Phys. Rev. X 8
2018
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T. Lan, C. Zhu, and X.-G. Wen, Fermion decoration construction of symmetry protected trivial orders for fermion systems with any symmetries G f G_{f} and in any dimensions (2018), a rXiv:1809.01112
2018
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Q.-R. Wang and Z.-C. 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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D. Gaiotto, T. Johnson-Freyd. Symmetry protected topological phases and generalized cohomology
2019
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T. Lan and X.-G. Wen, Classification of 3+1D Bosonic Topological Orders (II): The Case When Some Pointlike Excitations Are Fermions , Phys. Rev. X 9
2019
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A. Turzillo, M. You, Fermionic matrix product states and one-dimensional short-range entangled phases with antiunitary symmetries , Phys. Rev. B 99
2019
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Z. Wan, J. Wang, Higher Anomalies, Higher Symmetries, and Cobordisms I: Classification of Higher-Symmetry-Protected Topological States and Their Boundary Fermionic/Bosonic Anomalies via a Generalized Cobordism Theory
2019
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X.-G. Wen, Emergent (anomalous) higher symmetries from topological orders and from dynamical electromagnetic field in condensed matter systems
2019
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2019
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L. Kong, H. Zheng, A mathematical theory of gapless edges of 2d topological orders. Part I
2020
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L. Kong, Y. Tian, S. Zhou, The center of monoidal 2-categories in 3+1D Dijkgraaf-Witten Theory
2020
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