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Topological order in two dimensions can be described in terms of deconfined quasiparticle excitations - anyons - and their braiding statistics.
Lectures on tensor categories and modular functor
B. Bakalov and A. Kirillov · 2000
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Anyons in an exactly solved model and beyond
Alexei Kitaev · 2006
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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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Topological order with a twist: Ising anyons from an abelian model
H. Bombin · 2010
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Topological phases of fermions in one dimension
Lukasz Fidkowski and Alexei Kitaev · 2011
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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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Fractionalizing Majorana Fermions: Non-Abelian Statistics on the Edges of Abelian Quantum Hall States
N. H. Lindner, E. Berg, G. Refael, and A. Stern · 2012
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Models for Gapped Boundaries and Domain Walls
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Projective non-abelian statistics of dislocation defects in a 𝕫 N {\mathbb{z}}_{N} rotor model
Yi-Zhuang You and Xiao-Gang Wen · 2012
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Twist defects and projective non-abelian braiding statistics
Unconventional fusion and braiding of topological defects in a lattice model
Jeffrey C. Y. Teo, Abhishek Roy, and Xiao Chen · 2014
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Anyonic symmetries and topological defects in abelian topological phases: An application to the a d e ade classification
Mayukh Nilay Khan, Jeffrey C. Y. Teo, and Taylor L. Hughes · 2014
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Unpaired majorana modes on dislocations and string defects in kitaev’s honeycomb model
Olga Petrova, Paula Mellado, and Oleg Tchernyshyov · 2014
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to appear soon
Lukasz Fidkowski, Netanel H. Lindner, and Alexei Kitaev · 2014
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Symmetry, Defects, and Gauging of Topological Phases
M. Barkeshli, P. Bonderson, M. Cheng, and Z. Wang · 2014
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Anomalous Symmetry Fractionalization and Surface Topological Order
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Maissam Barkeshli, Chao-Ming Jian, and Xiao-Liang Qi · 2013
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Classification and properties of symmetry enriched topological phases: A chern-simons approach with applications to z2 spin liquids
Yuan-Ming Lu and Ashvin Vishwanath · 2013
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Changing topology by topological defects in three-dimensional topologically ordered phases
Andrej Mesaros, Yong Baek Kim, and Ying Ran · 2013
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Michael Hermele · 2014
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These fusion rules for defects in a permuting theory will generically be non-abelian
Cited in the paper.
To interpret ω ( g , h ) \omega(g,h) as a group cocycle, we also need to define its values when either g = 1 g=1 or h = 1 h=1 , which are cases that do not correspond to any plaquettes in our model. We simply set these equal to 1 1
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This is because any two solutions to eq. 81
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X. Chen, F. J. Burnell, A. Vishwanath, and L. Fidkowski · 2014
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’Gauging’ time reversal symmetry in tensor network states
X. Chen and A. Vishwanath · 2014
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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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