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We introduce the bilayer construction, as a specific purification scheme for a general mixed state, where each mixed state has a one-to-one correspondence with a bilayer pure state with two constraints: non-negativity of the bilayer wavefunction; and the presence of an anti-unitary layer-exchange symmetry T.
M. F. Atiyah, F. Hirzebruch, J. F. Adams, and G. C. Shepherd, Vector bundles and homogeneous spaces, in Algebraic Topology: A Student’s Guide , London Mathematical Society Lecture Note Series (Cambridge University Press, 1972) p. 196–222
1972
Earlier work this paper cites.
K. S. Brown, Equivariant homology and spectral sequences, in Cohomology of Groups (Springer New York, New York, NY, 1982) pp. 161–182
1982
Earlier work this paper cites.
R. E. Prange, Introduction, in The Quantum Hall Effect , edited by R. E. Prange and S. M. Girvin (Springer New York, New York, NY, 1990) pp. 1–35
1990
Earlier work this paper cites.
G. Baym and C. Pethick, Landau fermi-liquid theory and low temperature properties of normal liquid 3he, in Landau Fermi‐Liquid Theory (John Wiley & Sons, Ltd, 1991) Chap. 1, pp. 1–121, https://onlinelibrary.wiley.com/doi/pdf/10.1002/9783527617159.ch1
1991
Earlier work this paper cites.
A. Adem and R. J. Milgram, Spectral sequences and detection theorems, in Cohomology of Finite Groups (Springer Berlin Heidelberg, Berlin, Heidelberg, 1994) pp. 117–159
1994
Earlier work this paper cites.
X.-G. Wen, Topological orders and edge excitations in fractional quantum hall states, Advances in Physics 44
1995
Earlier work this paper cites.
A. H. Castro Neto, Charge Density Wave, Superconductivity, and Anomalous Metallic Behavior in 2D Transition Metal Dichalcogenides, Physical Review Letters 86
2001
Earlier work this paper cites.
E. Dennis, A. Kitaev, A. Landahl, and J. Preskill, Topological quantum memory, Journal of Mathematical Physics 43
2002
Earlier work this paper cites.
A. Kitaev, Fault-tolerant quantum computation by anyons, Annals of Physics 303
2003
Earlier work this paper cites.
M. A. Levin and X.-G. Wen, String-net condensation: A physical mechanism for topological phases, Phys. Rev. B 71
2005
Earlier work this paper cites.
E. Marino and L. H. Nunes, Quantum criticality and superconductivity in quasi-two-dimensional Dirac electronic systems, Nuclear Physics B 741
2006
Earlier work this paper cites.
E. Zhao and A. Paramekanti, BCS-BEC Crossover on the Two-Dimensional Honeycomb Lattice, Physical Review Letters 97
2006
Earlier work this paper cites.
A. Kitaev, Anyons in an exactly solved model and beyond, Annals of Physics 321
2006
Earlier work this paper cites.
A. Kitaev and J. Preskill, Topological entanglement entropy, Phys. Rev. Lett. 96
2006
Earlier work this paper cites.
M. Levin and X.-G. Wen, Detecting topological order in a ground state wave function, Phys. Rev. Lett. 96
2006
Earlier work this paper cites.
X.-G. Wen, Quantum Field Theory of Many-Body Systems: From the Origin of Sound to an Origin of Light and Electrons (Oxford University Press, 2007)
2007
Earlier work this paper cites.
B. Uchoa and A. H. Castro Neto, Superconducting States of Pure and Doped Graphene, Physical Review Letters 98
2007
Earlier work this paper cites.
C. Nayak, S. H. Simon, A. Stern, M. Freedman, and S. Das Sarma, Non-abelian anyons and topological quantum computation, Rev. Mod. Phys. 80
2008
Earlier work this paper cites.
H. Li and F. D. M. Haldane, Entanglement spectrum as a generalization of entanglement entropy: Identification of topological order in non-abelian fractional quantum hall effect states, Phys. Rev. Lett. 101
2008
Earlier work this paper cites.
M. Z. Hasan and C. L. Kane, Colloquium: Topological insulators, Rev. Mod. Phys. 82
2010
Earlier work this paper cites.
L. Balents, Spin liquids in frustrated magnets, Nature 464
2010
Earlier work this paper cites.
B. Roy and I. F. Herbut, Unconventional superconductivity on honeycomb lattice: Theory of Kekule order parameter, Physical Review B 82
2010
Earlier work this paper cites.
M. A. Nielsen and I. L. Chuang, Quantum computation and quantum information: 10th anniversary edition (Cambridge University Press, 2010)
2010
Earlier work this paper cites.
L. Fidkowski, Entanglement spectrum of topological insulators and superconductors, Phys. Rev. Lett. 104
2010
Earlier work this paper cites.
F. Pollmann, A. M. Turner, E. Berg, and M. Oshikawa, Entanglement spectrum of a topological phase in one dimension, Phys. Rev. B 81
2010
Earlier work this paper cites.
X.-L. Qi and S.-C. Zhang, Topological insulators and superconductors, Rev. Mod. Phys. 83
2011
Earlier work this paper cites.
M. Levin and Z.-C. Gu, Braiding statistics approach to symmetry-protected topological phases, Phys. Rev. B 86
2012
Earlier work this paper cites.
Y.-M. Lu and A. Vishwanath, Theory and classification of interacting integer topological phases in two dimensions: A chern-simons approach, Phys. Rev. B 86
2012
Earlier work this paper cites.
V. N. Kotov, B. Uchoa, V. M. Pereira, F. Guinea, and A. H. Castro Neto, Electron-Electron Interactions in Graphene: Current Status and Perspectives, Reviews of Modern Physics 84
2012
Earlier work this paper cites.
W. Son, L. Amico, and V. Vedral, Topological order in 1d cluster state protected by symmetry, Quantum Information Processing 11
2012
Earlier work this paper cites.
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
Cited alongside, same era.
A. M. Essin and M. Hermele, Classifying fractionalization: Symmetry classification of gapped 𝕫 2 {\mathbb{z}}_{2} spin liquids in two dimensions, Phys. Rev. B 87
2013
Cited alongside, same era.
A. Mesaros and Y. Ran, Classification of symmetry enriched topological phases with exactly solvable models, Phys. Rev. B 87
2013
Cited alongside, same era.
A. M. Black-Schaffer and C. Honerkamp, Chiral d
2014
Cited alongside, same era.
J. Eisenstein, Exciton condensation in bilayer quantum hall systems, Annual Review of Condensed Matter Physics 5
2014
Cited alongside, same era.
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R. Ma and C. Wang, Average symmetry-protected topological phases, Phys. Rev. X 13
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Cited alongside, same era.
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