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We introduce topological invariants for gapless systems and study the associated boundary phenomena.
Masuo Suzuki, “Relationship among Exactly Soluble Models of Critical Phenomena. I*)2D Ising Model, Dimer Problem and the Generalized XY-Model,” Progress of Theoretical Physics 46
1971
Earlier work this paper cites.
Amnon Aharony, “Critical Behavior of Anisotropic Cubic Systems,” Phys. Rev. B 8
1973
Earlier work this paper cites.
F. D. M. Haldane, “Continuum dynamics of the 1-D Heisenberg antiferromagnet: Identification with the O ( 3 ) O(3) nonlinear sigma model,” Phys. Lett. A 93
1983
Earlier work this paper cites.
A B Zamolodchikov and V A Fateev, “Nonlocal (parafermion) currents in two-dimensional conformal quantum field theory and self-dual critical points in Z N Z_{N} -symmetric statistical systems,” Sov. Phys. - JETP (Engl. Transl.); (United States) 62
1985
Earlier work this paper cites.
Cumrun Vafa, “Modular invariance and discrete torsion on orbifolds,” Nuclear Physics B 273
1986
Earlier work this paper cites.
G von Gehlen and V Rittenberg, “Operator content of the three-state Potts quantum chain,” Journal of Physics A: Mathematical and General 19
1986
Earlier work this paper cites.
Ian Affleck, Tom Kennedy, Elliott H. Lieb, and Hal Tasaki, “Valence bond ground states in isotropic quantum antiferromagnets,” Comm. Math. Phys. 115
1988
Earlier work this paper cites.
Robbert Dijkgraaf, Erik Verlinde, and Herman Verlinde, “ c = 1 c=1 conformal field theories on Riemann surfaces,” Comm. Math. Phys. 115
1988
Earlier work this paper cites.
P. Ginsparg, “Curiosities at c = 1 c=1 ,” Nuclear Physics B 295
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.
Elias B. Kiritsis, “Proof of the completeness of the classification of rational conformal theories with c=1,” Physics Letters B 217
1989
Earlier work this paper cites.
T Kennedy, “Exact diagonalisations of open spin-1 chains,” Journal of Physics: Condensed Matter 2
1990
Earlier work this paper cites.
P Ginsparg, “Applied conformal field theory.” in Les Houches, Session XLIX, 1988,Fields,Strings and Critical Phenomena , edited by E. Brezin and J. Zinn-Justin (Elsevier, 1990)
1990
Earlier work this paper cites.
Ian Affleck, “Field theory methods and quantum critical phenomena,” in Les Houches, Session XLIX, 1988,Fields,Strings and Critical Phenomena , edited by E. Brezin and J. Zinn-Justin (Elsevier, 1990)
1990
Earlier work this paper cites.
Tom Kennedy and Hal Tasaki, “Hidden symmetry breaking and the Haldane phase in S = 1 S=1 quantum spin chains,” Comm. Math. Phys. 147
1992
Earlier work this paper cites.
Steven R. White, “Density matrix formulation for quantum renormalization groups,” Phys. Rev. Lett. 69
1992
Earlier work this paper cites.
Kazuo Hida, “Crossover between the Haldane-gap phase and the dimer phase in the spin-1/2 alternating Heisenberg chain,” Phys. Rev. B 45
1992
Earlier work this paper cites.
M. Yamanaka, Y. Hatsugai, and M. Kohmoto, “Phase diagram of the S=1/2 quantum spin chain with bond alternation,” Phys. Rev. B 48
1993
Earlier work this paper cites.
D.M. McAvity and H. Osborn, “Energy-momentum tensor in conformal field theories near a boundary,” Nuclear Physics B 406
1993
Earlier work this paper cites.
Cumrun Vafa and Edward Witten, “On orbifolds with discrete torsion,” Journal of Geometry and Physics 15
1995
Earlier work this paper cites.
D.M. McAvity and H. Osborn, “Conformal field theories near a boundary in general dimensions,” Nuclear Physics B 455
1995
Earlier work this paper cites.
P. Di Francesco, P. Mathieu, and D. Senechal, Conformal Field Theory , Graduate Texts in Contemporary Physics (Springer-Verlag, New York, 1997)
1997
Earlier work this paper cites.
Michael R. Douglas, “D-branes and Discrete Torsion,” arXiv e-prints , hep-th/9807235 (1998), arXiv:hep-th/9807235 [hep-th]
1998
Earlier work this paper cites.
P. Ruelle and O. Verhoeven, “Discrete symmetries of unitary minimal conformal theories,” Nuclear Physics B 535
1998
Earlier work this paper cites.
José Manuel Carmona, Andrea Pelissetto, and Ettore Vicari, “ N N -component Ginzburg-Landau Hamiltonian with cubic anisotropy: A six-loop study,” Phys. Rev. B 61
2000
Earlier work this paper cites.
Robert Raussendorf and Hans J. Briegel, “A One-Way Quantum Computer,” Phys. Rev. Lett. 86
2001
Earlier work this paper cites.
G.M.T. Watts, “On the boundary Ising model with disorder operators,” Nuclear Physics B 596
2001
Earlier work this paper cites.
A Kitaev, “Unpaired Majorana fermions in quantum wires,” Physics-Uspekhi 44
2001
Earlier work this paper cites.
S. Sachdev, Quantum Phase Transitions (Cambridge University Press, 2001)
2001
Earlier work this paper cites.
Henk W. J. Blöte and Youjin Deng, “Cluster Monte Carlo simulation of the transverse Ising model,” Phys. Rev. E 66
2002
Earlier work this paper cites.
Wei Chen, Kazuo Hida, and B. C. Sanctuary, “Ground-state phase diagram of S = 1 S=1 XXZ \mathrm{XXZ} chains with uniaxial single-ion-type anisotropy,” Phys. Rev. B 67
2003
Earlier work this paper cites.
Eric Sharpe, “Discrete torsion,” Phys. Rev. D 68
2003
Earlier work this paper cites.
2003
Earlier work this paper cites.
T. Senthil, Ashvin Vishwanath, Leon Balents, Subir Sachdev, and Matthew P. A. Fisher, “Deconfined Quantum Critical Points,” Science 303
2004
Earlier work this paper cites.
J.P. Keating and F. Mezzadri, “Random matrix theory and entanglement in quantum spin chains,” Communications in Mathematical Physics 252
2004
Earlier work this paper cites.
T. Giamarchi, Quantum Physics in One Dimension , International Series of Monographs on Physics (Clarendon Press, 2004)
2004
Earlier work this paper cites.
G. Vidal, “Class of Quantum Many-Body States That Can Be Efficiently Simulated,” Phys. Rev. Lett. 101
2008
Earlier work this paper cites.
Zheng-Cheng Gu and Xiao-Gang Wen, “Tensor-entanglement-filtering renormalization approach and symmetry-protected topological order,” Phys. Rev. B 80
2009
Earlier work this paper cites.
R. Blumenhagen and E. Plauschinn, Introduction to Conformal Field Theory: With Applications to String Theory , Lecture Notes in Physics (Springer Berlin Heidelberg, 2009)
2009
Earlier work this paper cites.
2009
Earlier work this paper cites.
Frank Pollmann, Ari M. Turner, Erez Berg, and Masaki Oshikawa, “Entanglement spectrum of a topological phase in one dimension,” Phys. Rev. B 81
2010
Earlier work this paper cites.
Lukasz Fidkowski and Alexei Kitaev, “Topological phases of fermions in one dimension,” Phys. Rev. B 83
2011
Earlier work this paper cites.
Ari M. Turner, Frank Pollmann, and Erez Berg, “Topological phases of one-dimensional fermions: An entanglement point of view,” Phys. Rev. B 83
2011
Earlier work this paper cites.
Xie Chen, Zheng-Cheng Gu, and Xiao-Gang Wen, “Classification of gapped symmetric phases in one-dimensional spin systems,” Phys. Rev. B 83
2011
Earlier work this paper cites.
Schuch, N. and Pérez-García, D. and Cirac, J. I., “Classifying quantum phases using matrix product states and projected entangled pair states,” Phys. Rev. B 84
2011
Earlier work this paper cites.
J. P. Kestner, Bin Wang, Jay D. Sau, and S. Das Sarma, “Prediction of a gapless topological Haldane liquid phase in a one-dimensional cold polar molecular lattice,” Phys. Rev. B 83
2011
Earlier work this paper cites.
Meng Cheng and Hong-Hao Tu, “Majorana edge states in interacting two-chain ladders of fermions,” Phys. Rev. B 84
2011
Cited alongside, same era.
Lukasz Fidkowski, Roman M. Lutchyn, Chetan Nayak, and Matthew P. A. Fisher, “Majorana zero modes in one-dimensional quantum wires without long-ranged superconducting order,” Phys. Rev. B 84
2011
Cited alongside, same era.
Jay D. Sau, B. I. Halperin, K. Flensberg, and S. Das Sarma, “Number conserving theory for topologically protected degeneracy in one-dimensional fermions,” Phys. Rev. B 84
2011
Cited alongside, same era.
W. Son, L. Amico, R. Fazio, A. Hamma, S. Pascazio, and V. Vedral, “Quantum phase transition between cluster and antiferromagnetic states,” EPL (Europhysics Letters) 95
2011
Cited alongside, same era.
2016
Later among the works it cites.
Michael Schuler, Seth Whitsitt, Louis-Paul Henry, Subir Sachdev, and Andreas M. Läuchli, “Universal Signatures of Quantum Critical Points from Finite-Size Torus Spectra: A Window into the Operator Content of Higher-Dimensional Conformal Field Theories,” Phys. Rev. Lett. 117
2016
Later among the works it cites.
Beni Yoshida, “Topological phases with generalized global symmetries,” Phys. Rev. B 93
2016
Later among the works it cites.
Arianna Montorsi, Fabrizio Dolcini, Rita C. Iotti, and Fausto Rossi, “Symmetry-protected topological phases of one-dimensional interacting fermions with spin-charge separation,” Phys. Rev. B 95
2017
Later among the works it cites.
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2011
Cited alongside, same era.
2011
Cited alongside, same era.
Martin Hasenbusch and Ettore Vicari, “Anisotropic perturbations in three-dimensional o( n n )-symmetric vector models,” Phys. Rev. B 84
2011
Cited alongside, same era.
J. Ruhman, E. G. Dalla Torre, S. D. Huber, and E. Altman, “Nonlocal order in elongated dipolar gases,” Phys. Rev. B 85
2012
Cited alongside, same era.
2012
Cited alongside, same era.
Frank Pollmann and Ari M. Turner, “Detection of symmetry-protected topological phases in one dimension,” Phys. Rev. B 86
2012
Cited alongside, same era.
Michael Levin and Zheng-Cheng Gu, “Braiding statistics approach to symmetry-protected topological phases,” Phys. Rev. B 86
2012
Cited alongside, same era.
2012
Cited alongside, same era.
Zhiyuan Wang, Youjiang Xu, Han Pu, and Kaden R. A. Hazzard, “Number-conserving interacting fermion models with exact topological superconducting ground states,” Phys. Rev. B 96
2017
Later among the works it cites.
Jonathan Ruhman and Ehud Altman, “Topological degeneracy and pairing in a one-dimensional gas of spinless fermions,” Phys. Rev. B 96
2017
Later among the works it cites.
Thomas Scaffidi, Daniel E. Parker, and Romain Vasseur, “Gapless Symmetry-Protected Topological Order,” Phys. Rev. X 7
2017
Later among the works it cites.
K. Guther, N. Lang, and H. P. Büchler, “Ising anyonic topological phase of interacting fermions in one dimension,” Phys. Rev. B 96
2017
Later among the works it cites.
Nikolaos Kainaris, Raul A. Santos, D. B. Gutman, and Sam T. Carr, “Interaction induced topological protection in one-dimensional conductors,” Fortschritte der Physik 65
2017
Later among the works it cites.
Ruben Verresen, Roderich Moessner, and Frank Pollmann, “One-dimensional symmetry protected topological phases and their transitions,” Phys. Rev. B 96
2017
Later among the works it cites.
Kristian Patrick, Titus Neupert, and Jiannis K. Pachos, “Topological Quantum Liquids with Long-Range Couplings,” Phys. Rev. Lett. 118
2017
Later among the works it cites.
Lokman Tsui, Yen-Ta Huang, Hong-Chen Jiang, and Dung-Hai Lee, “The phase transitions between Z n × Z n Z_{n}\times Z_{n} bosonic topological phases in 1+1D, and a constraint on the central charge for the critical points between bosonic symmetry protected topological phases,” Nuclear Physics B 919
2017
Later among the works it cites.
D. Meidan, E. Berg, and Ady Stern, “Classification of topological phases of parafermionic chains with symmetries,” Phys. Rev. B 95
2017
Later among the works it cites.
Alex Thomson and Subir Sachdev, “Spectrum of conformal gauge theories on a torus,” Phys. Rev. B 95
2017
Later among the works it cites.
Seth Whitsitt, Michael Schuler, Louis-Paul Henry, Andreas M. Läuchli, and Subir Sachdev, “Spectrum of the Wilson-Fisher conformal field theory on the torus,” Phys. Rev. B 96
2017
Later among the works it cites.
Beni Yoshida, “Gapped boundaries, group cohomology and fault-tolerant logical gates,” Annals of Physics 377
2017
Later among the works it cites.
Long Zhang and Fa Wang, “Unconventional Surface Critical Behavior Induced by a Quantum Phase Transition from the Two-Dimensional Affleck-Kennedy-Lieb-Tasaki Phase to a Néel-Ordered Phase,” Phys. Rev. Lett. 118
2017
Later among the works it cites.
Nikhil Anand, Vincent X. Genest, Emanuel Katz, Zuhair U. Khandker, and Matthew T. Walters, “RG flow from φ 4 \varphi^{4} theory to the 2D Ising model,” Journal of High Energy Physics 2017
2017
Later among the works it cites.
Hong-Chen Jiang, Zi-Xiang Li, Alexander Seidel, and Dung-Hai Lee, “Symmetry protected topological Luttinger liquids and the phase transition between them,” Science Bulletin 63
2018
Later among the works it cites.
Rui-Xing Zhang and Chao-Xing Liu, “Crystalline Symmetry-Protected Majorana Mode in Number-Conserving Dirac Semimetal Nanowires,” Phys. Rev. Lett. 120
2018
Later among the works it cites.
Ruben Verresen, Nick G. Jones, and Frank Pollmann, “Topology and Edge Modes in Quantum Critical Chains,” Phys. Rev. Lett. 120
2018
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Daniel E. Parker, Thomas Scaffidi, and Romain Vasseur, “Topological Luttinger liquids from decorated domain walls,” Phys. Rev. B 97
2018
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Anna Keselman, Erez Berg, and Patrick Azaria, “From one-dimensional charge conserving superconductors to the gapless Haldane phase,” Phys. Rev. B 98
2018
Later among the works it cites.
Chun Chen, Wei Yan, C. S. Ting, Yan Chen, and F. J. Burnell, “Flux-stabilized Majorana zero modes in coupled one-dimensional Fermi wires,” Phys. Rev. B 98
2018
Later among the works it cites.
Apoorv Tiwari, Xiao Chen, Ken Shiozaki, and Shinsei Ryu, “Bosonic topological phases of matter: Bulk-boundary correspondence, symmetry protected topological invariants, and gauging,” Phys. Rev. B 97
2018
Later among the works it cites.
Satoshi Ejima, Tomoki Yamaguchi, Fabian H. L. Essler, Florian Lange, Yukinori Ohta, and Holger Fehske, “Exotic criticality in the dimerized spin-1 X X Z XXZ chain with single-ion anisotropy,” SciPost Phys. 5
2018
Later among the works it cites.
2018
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Alexandre Belin, Jan de Boer, and Jorrit Kruthoff, “Comments on a state-operator correspondence for the torus,” SciPost Phys. 5
2018
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Lukas Weber, Francesco Parisen Toldin, and Stefan Wessel, “Nonordinary edge criticality of two-dimensional quantum critical magnets,” Phys. Rev. B 98
2018
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Shenghan Jiang and Olexei Motrunich, “Ising ferromagnet to valence bond solid transition in a one-dimensional spin chain: Analogies to deconfined quantum critical points,” Phys. Rev. B 99
2019
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N. G. Jones and R. Verresen, “Asymptotic Correlations in Gapped and Critical Topological Phases of 1D Quantum Systems,” Journal of Statistical Physics 175
2019
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Daniel E. Parker, Romain Vasseur, and Thomas Scaffidi, “Topologically Protected Long Edge Coherence Times in Symmetry-Broken Phases,” Phys. Rev. Lett. 122
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