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We present a hierarchy of quantum many-body states among which many examples of topological order can be identified by construction.
Finite ring groups
G. I. Kac and V. G. Paljutkin · 1966
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The resonating valence bond state in La 2 CuO 4 \text{La}_{2}\text{CuO}_{4} and superconductivity
Philip W. Anderson · 1987
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Quantum groups
Vladimir G. Drinfeld · 1987
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Topological quantum field theory
Edward Witten · 1988
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Finitely correlated states on quantum spin chains
Mark Fannes, Bruno Nachtergaele, and Reinhard F. Werner · 1992
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Topological phases of quantum theories. Chern-Simons theory
Manuel Asorey · 1993
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Christian Kassel · 1995
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Akira Masuoka · 1995
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Density matrix renormalization group method for 2D classical models
Tomotoshi Nishino · 1995
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Hans-Jürgen Schneider · 1995
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Topological orders and edge excitations in fractional quantum Hall states
Xiao-Gang Wen · 1995
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Akira Masuoka · 1996
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Anatoli Klimyk and Konrad Schmüdgen · 1997
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Quantum chains of Hopf algebras with quantum double cosymmetry
Florian Nill and Kornél Szlachányi · 1997
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Quantum codes on a lattice with boundary, 1998
Sergey Bravyi and Alexei Y. Kitaev · 1998
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Semisimple Hopf algebras of dimension p q pq are trivial
Pavel Etingof and Shlomo Gelaki · 1998
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Broken quantum symmetry and confinement phases in planar physics
F. Alexander Bais, Bernd J. Schroers, and Joost K. Slingerland · 2002
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Eric Dennis, Alexei Y. Kitaev, Andrew Landahl, and John Preskill · 2002
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Michael H. Freedman, Michael J. Larsen, and Zhenghan Wang · 2002
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Variational study of hard-core bosons in a two-dimensional optical lattice using projected entangled pair states
Valentin Murg, Frank Verstraete, and J. Ignacio Cirac · 2007
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Entanglement renormalization
Guifré Vidal · 2007
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Miguel Aguado and Guifré Vidal · 2008
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Many-body physics with ultracold gases
Immanuel Bloch, Jean Dalibard, and Wilhelm Zwerger · 2008
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Class of quantum many-body states that can be efficiently simulated
Guifré Vidal · 2008
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Mapping Kitaev’s quantum double lattice models to Levin and Wen’s string-net models
Oliver Buerschaper and Miguel Aguado · 2009
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Frank Verstraete and J. Ignacio Cirac · 2004
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Valence-bond states for quantum computation
Frank Verstraete and J. Ignacio Cirac · 2004
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Michael A. Levin and Xiao-Gang Wen · 2005
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Oliver Buerschaper, Miguel Aguado, and Guifré Vidal · 2009
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Exact entanglement renormalization for string-net models
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A short proof of stability of topological order under local perturbations, 2010
Sergey Bravyi and Matthew B. Hastings · 2010
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