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The hallmark of a 2 dimensional topologically ordered phase is the existence of deconfined `anyon' excitations that have exotic braiding and exchange statistics, different from those of ordinary bosons or fermions.
Topological gauge theories and group cohomology
Robbert Dijkgraaf and Edward Witten · 1990
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Fusion categories and homotopy theory
P. Etingof, D. Nikshych, V. Ostrik, and w. a. a. b. Ehud Meir · 2009
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On braided fusion categories I
V. Drinfeld, S. Gelaki, D. Nikshych, and V. Ostrik · 2009
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Entanglement spectrum of a topological phase in one dimension
Frank Pollmann, Ari M. Turner, Erez Berg, and Masaki Oshikawa · 2010
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Classification of gapped symmetric phases in one-dimensional spin systems
X. Chen, Z.-C. Gu, and X.-G. Wen · 2011
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Topological phases of fermions in one dimension
Lukasz Fidkowski and Alexei Kitaev · 2011
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Braiding statistics approach to symmetry-protected topological phases
Michael Levin and Zheng-Cheng Gu · 2012
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Symmetry protected topological orders and the group cohomology of their symmetry group
Xie Chen, Zheng-Cheng Gu, Zheng-Xin Liu, and Xiao-Gang Wen · 2013
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Symmetry protected topological orders and the group cohomology of their symmetry group
Xie Chen, Zheng-Cheng Gu, Zheng-Xin Liu, and Xiao-Gang Wen · 2013
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Classifying fractionalization: Symmetry classification of gapped 𝕫 2 {\mathbb{z}}_{2} spin liquids in two dimensions
Andrew M. Essin and Michael Hermele · 2013
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Classification of symmetry enriched topological phases with exactly solvable models
Andrej Mesaros and Ying Ran · 2013
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Non-abelian topological order on the surface of a 3d topological superconductor from an exactly solved model
Lukasz Fidkowski, Xie Chen, and Ashvin Vishwanath · 2013
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Symmetry protected topological phases from decorated domain walls
Xie Chen, Yuan-Ming Lu, and Ashvin Vishwanath · 2013
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Classification and description of bosonic symmetry protected topological phases with semiclassical nonlinear sigma models
Zhen Bi, Alex Rasmussen, and Cenke Xu · 2013
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Theory of Twist Liquids: Gauging an Anyonic Symmetry
J. C. Y. Teo, T. L. Hughes, and E. Fradkin · 2015
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Symmetry fractionalization and twist defects
N. Tarantino, N. Lindner, and L. Fidkowski · 2015
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Anomalous symmetry fractionalization and surface topological order
Xie Chen, F. J. Burnell, Ashvin Vishwanath, and Lukasz Fidkowski · 2015
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Bosonic topological crystalline insulators and anomalous symmetry fractionalization via the flux-fusion anomaly test
M. Hermele and X. Chen · 2015
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Generalized global symmetries
D. Gaiotto, A. Kapustin, N. Seiberg, and B. Willett · 2015
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to appear, 2015
R. Thorngren and A. von Keyserlingk · 2015
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Braiding statistics of loop excitations in three dimensions
C. Wang and M. Levin · 2014
Cited alongside, same era.
Symmetry, Defects, and Gauging of Topological Phases
M. Barkeshli, P. Bonderson, M. Cheng, and Z. Wang · 2014
Cited alongside, same era.
Symmetry enforced non-abelian topological order at the surface of a topological insulator
Xie Chen, Lukasz Fidkowski, and Ashvin Vishwanath · 2014
Cited alongside, same era.
String flux mechanism for fractionalization in topologically ordered phases
Michael Hermele · 2014
Cited alongside, same era.
More formally, this screening corresponds to a 2-cochain of ℤ 2 G \mathbb{Z}_{2}^{G} , and involves a modification of the ℤ 2 G \mathbb{Z}_{2}^{G} flux fusion rule by m = 2 m=2
Cited in the paper.
More precisely, they induce a trivial braided tensor automorphism of the quasiparticles
Cited in the paper.
Recall that the center of a group H H is defined as the set of all z ∈ H z\in H which commute with all of H H , i.e. z h = h z zh=hz for all h ∈ H h\in H
Cited in the paper.
http://sierra.nmsu.edu/morandi/notes/GroupExtensions.pdf
Group extensions and h 3 h^{3} · 2015
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Space group symmetry fractionalization in a chiral kagome heisenberg antiferromagnet
Michael P. Zaletel, Zhenyue Zhu, Yuan-Ming Lu, Ashvin Vishwanath, and Steven R. White · 2016
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