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We introduce exactly solvable gapless quantum systems in $d$ dimensions that support symmetry protected topological (SPT) edge modes.
J. Ashkin and E. Teller, “Statistics of Two-Dimensional Lattices with Four Components,” Phys. Rev. 64
1943
Earlier work this paper cites.
G. H. Wannier, “Antiferromagnetism. The Triangular Ising Net,” Phys. Rev. 79
1950
Earlier work this paper cites.
Eduardo Fradkin and Stephen H. Shenker, “Phase diagrams of lattice gauge theories with Higgs fields,” Phys. Rev. D 19
1979
Earlier work this paper cites.
W. J. L Buyers, R. M. Morra, R. L. Armstrong, M. J. Hogan, P. Gerlach, and K. Hirakawa, “Experimental evidence for the Haldane gap in a spin-1 nearly isotropic, antiferromagnetic chain,” Phys. Rev. Lett. 56
1986
Earlier work this paper cites.
Alexander B Zamolodchikov, “Irreversibility of the Flux of the Renormalization Group in a 2D Field Theory,” JETP lett 43
1986
Earlier work this paper cites.
F. D. M. Haldane, “O(3) Nonlinear σ \sigma Model and the Topological Distinction between Integer- and Half-Integer-Spin Antiferromagnets in Two Dimensions,” Phys. Rev. Lett. 61
1988
Earlier work this paper cites.
Daniel S Rokhsar and Steven A Kivelson, “Superconductivity and the quantum hard-core dimer gas,” Physical Review Letters 61
1988
Earlier work this paper cites.
John L. Cardy, “Boundary conditions, fusion rules and the Verlinde formula,” Nuclear Physics B 324
1989
Earlier work this paper cites.
S. Fubini and C. A. Lutken, “Vertex Operators in the Fraction Quantum Hall Effect,” Modern Physics Letters A 06
1991
Earlier work this paper cites.
Gregory Moore and Nicholas Read, “Nonabelions in the fractional quantum hall effect,” Nuclear Physics B 360
1991
Earlier work this paper cites.
Tom Kennedy and Hal Tasaki, “Hidden symmetry breaking and the Haldane phase in S=1 quantum spin chains,” Communications in Mathematical Physics 147
1992
Earlier work this paper cites.
S. R. White, “Density-matrix formulation for quantum renormalization groups,” Phys. Rev. Lett. 69
1992
Earlier work this paper cites.
Daniel S. Fisher, “Random transverse field Ising spin chains,” Phys. Rev. Lett. 69
1992
Earlier work this paper cites.
B. Blok and X.G. Wen, “Many-body systems with non-abelian statistics,” Nuclear Physics B 374
1992
Earlier work this paper cites.
B. I. Halperin, Patrick A. Lee, and Nicholas Read, “Theory of the half-filled Landau level,” Phys. Rev. B 47
1993
Earlier work this paper cites.
R. Chatterjee and A. Zamolodchikov, “Local Magnetization in Critical Ising Model with Boundary Magenetic Field,” Modern Physics Letters A 09
1994
Earlier work this paper cites.
Daniel S. Fisher, “Random antiferromagnetic quantum spin chains,” Phys. Rev. B 50
1994
Earlier work this paper cites.
H. W. J. Blote and B. Nienhuis, “Fully packed loop model on the honeycomb lattice,” Phys. Rev. Lett. 72
1994
Earlier work this paper cites.
Jané Kondev, Jan de Gier, and Bernard Nienhuis, “Operator spectrum and exact exponents of the fully packed loop model,” Journal of Physics A: Mathematical and General 29
1996
Earlier work this paper cites.
M T Batchelor, H W J Blöte, B Nienhuis, and C M Yung, “Critical behaviour of the fully packed loop model on the square lattice,” Journal of Physics A: Mathematical and General 29
1996
Earlier work this paper cites.
Ian Affleck, “Edge magnetic field in the XXZ spin- 1 2 \frac{1}{2} chain,” Journal of Physics A: Mathematical and General 31
1998
Earlier work this paper cites.
Xiao-Gang Wen, “Quantum orders and symmetric spin liquids,” Phys. Rev. B 65
2002
Earlier work this paper cites.
P. Lecheminant, Alexander O. Gogolin, and Alexander A. Nersesyan, “Criticality in self-dual sine-Gordon models,” Nuclear Physics B 639
2002
Earlier work this paper cites.
X. G. Wen and A. Zee, “Gapless fermions and quantum order,” Phys. Rev. B 66
2002
Earlier work this paper cites.
Grigory E Volovik, The universe in a helium droplet , Vol. 117 (Oxford University Press on Demand, 2003)
2003
Earlier work this paper cites.
T. Giamarchi, Quantum Physics in One Dimension , International Series of Monographs on Physics (Clarendon Press, 2003)
2003
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 Graduate Texts (OUP Oxford, 2004)
2004
Earlier work this paper cites.
Eddy Ardonne, Paul Fendley, and Eduardo Fradkin, “Topological order and conformal quantum critical points,” Annals of Physics 310
2004
Earlier work this paper cites.
Eduardo Fradkin, David A. Huse, R. Moessner, V. Oganesyan, and S. L. Sondhi, “Bipartite Rokhsar-Kivelson points and Cantor deconfinement,” Phys. Rev. B 69
2004
Earlier work this paper cites.
Ashvin Vishwanath, L. Balents, and T. Senthil, “Quantum criticality and deconfinement in phase transitions between valence bond solids,” Phys. Rev. B 69
2004
Earlier work this paper cites.
Pasquale Calabrese and John Cardy, “Entanglement entropy and quantum field theory,” Journal of Statistical Mechanics: Theory and Experiment 2004
2004
Earlier work this paper cites.
Michael Hermele, Matthew P. A. Fisher, and Leon Balents, “Pyrochlore photons: The U ( 1 ) U(1) spin liquid in a S = 1 2 S=\frac{1}{2} three-dimensional frustrated magnet,” Phys. Rev. B 69
2004
Earlier work this paper cites.
C. L. Kane and E. J. Mele, “Quantum Spin Hall Effect in Graphene,” Phys. Rev. Lett. 95
2005
Earlier work this paper cites.
Alexei Kitaev and John Preskill, “Topological Entanglement Entropy,” Phys. Rev. Lett. 96
2006
Earlier work this paper cites.
Michael Levin and Xiao-Gang Wen, “Detecting Topological Order in a Ground State Wave Function,” Phys. Rev. Lett. 96
2006
Earlier work this paper cites.
B. Andrei Bernevig, Taylor L. Hughes, and Shou-Cheng Zhang, “Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells,” Science 314
2006
Earlier work this paper cites.
Eduardo Fradkin and Joel E. Moore, “Entanglement Entropy of 2D Conformal Quantum Critical Points: Hearing the Shape of a Quantum Drum,” Phys. Rev. Lett. 97
2006
Earlier work this paper cites.
Markus Konig, Steffen Wiedmann, Christoph Brune, Andreas Roth, Hartmut Buhmann, Laurens W. Molenkamp, Xiao-Liang Qi, and Shou-Cheng Zhang, “Quantum Spin Hall Insulator State in HgTe Quantum Wells,” Science 318
2007
Earlier work this paper cites.
Liang Fu, C. L. Kane, and E. J. Mele, “Topological Insulators in Three Dimensions,” Phys. Rev. Lett. 98
2007
Earlier work this paper cites.
J. E. Moore and L. Balents, “Topological invariants of time-reversal-invariant band structures,” Phys. Rev. B 75
2007
Earlier work this paper cites.
Steven H. Simon, E. H. Rezayi, N. R. Cooper, and I. Berdnikov, “Construction of a paired wave function for spinless electrons at filling fraction ν = 2 / 5 \nu=2/5 ,” Phys. Rev. B 75
2007
Earlier work this paper cites.
D. Hsieh, D. Qian, L. Wray, Y. Xia, Y. S. Hor, R. J. Cava, and M. Z. Hasan, “A topological Dirac insulator in a quantum spin Hall phase,” Nature 452
2008
Earlier work this paper cites.
Andreas P. Schnyder, Shinsei Ryu, Akira Furusaki, and Andreas W. W. Ludwig, “Classification of topological insulators and superconductors in three spatial dimensions,” Phys. Rev. B 78
2008
Earlier work this paper cites.
Chetan Nayak, Steven H. Simon, Ady Stern, Michael Freedman, and Sankar Das Sarma, “Non-Abelian anyons and topological quantum computation,” Rev. Mod. Phys. 80
2008
Cited alongside, same era.
Hui 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
Cited alongside, same era.
Luigi Amico, Rosario Fazio, Andreas Osterloh, and Vlatko Vedral, “Entanglement in many-body systems,” Rev. Mod. Phys. 80
2008
Cited alongside, same era.
Rahul Roy, “Topological phases and the quantum spin Hall effect in three dimensions,” Phys. Rev. B 79
2009
Cited alongside, same era.
Zheng-Cheng Gu and Xiao-Gang Wen, “Tensor-entanglement-filtering renormalization approach and symmetry-protected topological order,” Phys. Rev. B 80
Chong Wang, Andrew C. Potter, and T. Senthil, “Classification of Interacting Electronic Topological Insulators in Three Dimensions,” Science 343
2014
Later among the works it cites.
Zheng-Cheng Gu and Xiao-Gang Wen, “Symmetry-protected topological orders for interacting fermions: Fermionic topological nonlinear σ \sigma models and a special group supercohomology theory,” Phys. Rev. B 90
2014
Later among the works it cites.
Hendrik Weimer, “String order in dipole-blockaded quantum liquids,” New Journal of Physics 16
2014
Later among the works it cites.
Xie Chen, Yuan-Ming Lu, and Ashvin Vishwanath, “Symmetry-protected topological phases from decorated domain walls,” Nat Commun 5
2014
Later among the works it cites.
David Pekker, Gil Refael, Ehud Altman, Eugene Demler, and Vadim Oganesyan, “Hilbert-Glass Transition: New Universality of Temperature-Tuned Many-Body Dynamical Quantum Criticality,” Phys. Rev. X 4
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2009
Cited alongside, same era.
Alexei Kitaev, “Periodic table for topological insulators and superconductors,” AIP Conference Proceedings 1134
2009
Cited alongside, same era.
J.L. Jacobsen, “Polygons, Polyominoes and Polycubes,” (Springer Netherlands, 2009) Chap. Conformal Field Theory Applied to Loop Models
2009
Cited alongside, same era.
Pasquale Calabrese and John Cardy, “Entanglement entropy and conformal field theory,” Journal of Physics A: Mathematical and Theoretical 42
2009
Cited alongside, same era.
Jean-Marie Stéphan, Shunsuke Furukawa, Grégoire Misguich, and Vincent Pasquier, “Shannon and entanglement entropies of one- and two-dimensional critical wave functions,” Phys. Rev. B 80
2009
Cited alongside, same era.
Joseph Maciejko, Xiao-Liang Qi, Andreas Karch, and Shou-Cheng Zhang, “Fractional Topological Insulators in Three Dimensions,” Phys. Rev. Lett. 105
2010
Cited alongside, same era.
M Zahid Hasan and Charles L Kane, “Colloquium: topological insulators,” Reviews of Modern Physics 82
2010
Cited alongside, same era.
Lukasz Fidkowski and Alexei Kitaev, “Effects of interactions on the topological classification of free fermion systems,” Phys. Rev. B 81
2010
Cited alongside, same era.
2014
Later among the works it cites.
Ronen Vosk and Ehud Altman, “Dynamical Quantum Phase Transitions in Random Spin Chains,” Phys. Rev. Lett. 112
2014
Later among the works it cites.
Adam S. Jermyn, Roger S. K. Mong, Jason Alicea, and Paul Fendley, “Stability of zero modes in parafermion chains,” Phys. Rev. B 90
2014
Later among the works it cites.
Yi-Zhuang You, Zhen Bi, Alex Rasmussen, Kevin Slagle, and Cenke Xu, “Wave Function and Strange Correlator of Short-Range Entangled States,” Phys. Rev. Lett. 112
2014
Later among the works it cites.
Wei Li, Shuo Yang, Meng Cheng, Zheng-Xin Liu, and Hong-Hao Tu, “Topology and criticality in the resonating Affleck-Kennedy-Lieb-Tasaki loop spin liquid states,” Phys. Rev. B 89
2014
Later among the works it cites.
Zhen Bi, Alex Rasmussen, Kevin Slagle, and Cenke Xu, “Classification and description of bosonic symmetry protected topological phases with semiclassical nonlinear sigma models,” Phys. Rev. B 91
2015
Later among the works it cites.
2015
Later among the works it cites.
Yasaman Bahri, Ronen Vosk, Ehud Altman, and Ashvin Vishwanath, “Localization and topology protected quantum coherence at the edge of hot matter,” Nature Communications 6
2015
Later among the works it cites.
B. Q. Lv, H. M. Weng, B. B. Fu, X. P. Wang, H. Miao, J. Ma, P. Richard, X. C. Huang, L. X. Zhao, G. F. Chen, Z. Fang, X. Dai, T. Qian, and H. Ding, “Experimental Discovery of Weyl Semimetal TaAs,” Phys. Rev. X 5
2015
Later among the works it cites.
Ling Lu, Zhiyu Wang, Dexin Ye, Lixin Ran, Liang Fu, John D. Joannopoulos, and Marin Soljačić, “Experimental observation of Weyl points,” Science 349
2015
Later among the works it cites.
Su-Yang Xu, Ilya Belopolski, Nasser Alidoust, Madhab Neupane, Guang Bian, Chenglong Zhang, Raman Sankar, Guoqing Chang, Zhujun Yuan, Chi-Cheng Lee, et al. , “Discovery of a weyl fermion semimetal and topological fermi arcs,” Science 349
2015
Later among the works it cites.
Jonathan Ruhman, Erez Berg, and Ehud Altman, “Topological States in a One-Dimensional Fermi Gas with Attractive Interaction,” Phys. Rev. Lett. 114
2015
Later among the works it cites.
Anna Keselman and Erez Berg, “Gapless symmetry-protected topological phase of fermions in one dimension,” Phys. Rev. B 91
2015
Later among the works it cites.
Dam Thanh Son, “Is the Composite Fermion a Dirac Particle?” Phys. Rev. X 5
2015
Later among the works it cites.
2015
Later among the works it cites.
Zohar Ringel and Steven H. Simon, “Hidden order and flux attachment in symmetry-protected topological phases: A Laughlin-like approach,” Phys. Rev. B 91
2015
Later among the works it cites.
2015
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Lokman Tsui, Hong-Chen Jiang, Yuan-Ming Lu, and Dung-Hai Lee, “Quantum phase transitions between a class of symmetry protected topological states,” Nuclear Physics B 896
2015
Later among the works it cites.
R. Vasseur, A. C. Potter, and S. A. Parameswaran, “Quantum Criticality of Hot Random Spin Chains,” Phys. Rev. Lett. 114
2015
Later among the works it cites.
Maissam Barkeshli, Michael Mulligan, and Matthew P. A. Fisher, “Particle-hole symmetry and the composite Fermi liquid,” Phys. Rev. B 92
2015
Later among the works it cites.
Chong Wang, Adam Nahum, and T. Senthil, “Topological paramagnetism in frustrated spin-1 Mott insulators,” Phys. Rev. B 91
2015
Later among the works it cites.
Yuan-Ming Lu and Ashvin Vishwanath, “Classification and properties of symmetry-enriched topological phases: Chern-Simons approach with applications to Z 2 {Z}_{2} spin liquids,” Phys. Rev. B 93
2016
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2016
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Beni Yoshida, “Topological phases with generalized global symmetries,” Phys. Rev. B 93
2016
Later among the works it cites.
Yizhi You and Yi-Zhuang You, “Stripe melting and a transition between weak and strong symmetry protected topological phases,” Phys. Rev. B 93
2016
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Paul Fendley, “Strong zero modes and eigenstate phase transitions in the XYZ/interacting Majorana chain,” Journal of Physics A: Mathematical and Theoretical 49
2016
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Didier Poilblanc, Norbert Schuch, and Ian Affleck, “ SU ( 2 ) 1 \mathrm{SU}(2{)}_{1} chiral edge modes of a critical spin liquid,” Phys. Rev. B 93
2016
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Michael Mulligan, S. Raghu, and Matthew P. A. Fisher, “Emergent particle-hole symmetry in the half-filled Landau level,” Phys. Rev. B 94
2016
Later among the works it cites.
Thomas Scaffidi and Zohar Ringel, “Wave functions of symmetry-protected topological phases from conformal field theories,” Phys. Rev. B 93
2016
Later among the works it cites.
Brayden Ware, Jun Ho Son, Meng Cheng, Ryan V. Mishmash, Jason Alicea, and Bela Bauer, “Ising anyons in frustration-free Majorana-dimer models,” Phys. Rev. B 94
2016
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Nicolas Tarantino and Lukasz Fidkowski, “Discrete spin structures and commuting projector models for two-dimensional fermionic symmetry-protected topological phases,” Phys. Rev. B 94
2016
Later among the works it cites.
Chong Wang and T. Senthil, “Time-Reversal Symmetric U ( 1 ) U(1) Quantum Spin Liquids,” Phys. Rev. X 6
2016
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2017
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2017
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2017
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2017
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2017
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2017
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