Built on

Yang-Zhi Chou, Rahul M. Nandkishore, and Leo Radzihovsky, “Localized surfaces of three-dimensional topological insulators,” Phys. Rev. B 99
Original
1901
Earlier work this paper cites.
Itamar Kimchi, Yang-Zhi Chou, Rahul M. Nandkishore, and Leo Radzihovsky, “Anomalous localization at the boundary of an interacting topological insulator,” Phys. Rev. B 101
Original
1909
Earlier work this paper cites.
Elliott Lieb, Theodore Schultz, and Daniel Mattis, “Two soluble models of an antiferromagnetic chain,” Annals of Physics 16
1961
Earlier work this paper cites.
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.
Yoseph Imry and Shang-keng Ma, “Random-field instability of the ordered state of continuous symmetry,” Phys. Rev. Lett. 35
1975
Earlier work this paper cites.
Shang-keng Ma, Chandan Dasgupta, and Chin-kun Hu, “Random antiferromagnetic chain,” Physical review letters 43
1979
Earlier work this paper cites.
L. D. Landau and E. M. Lifshitz, Statistical Physics, Part 1 , Course of Theoretical Physics, Vol. 5 (Butterworth-Heinemann, Oxford, 1980)
1980
Earlier work this paper cites.
Chandan Dasgupta and Shang-keng Ma, “Low-temperature properties of the random heisenberg antiferromagnetic chain,” Physical review b 22
1980
Earlier work this paper cites.
D. J. Thouless, “Quantization of particle transport,” Phys. Rev. B 27
1983
Earlier work this paper cites.
P. A. Lee and A. Douglas Stone, “Universal conductance fluctuations in metals,” Phys. Rev. Lett. 55
1985
Earlier work this paper cites.
Steven R White, “Density matrix formulation for quantum renormalization groups,” Physical review letters 69
1992
Earlier work this paper cites.
Daniel S Fisher, “Random antiferromagnetic quantum spin chains,” Physical review b 50
1994
Earlier work this paper cites.
John Preskill, “Lecture notes for physics 229: Quantum information and computation,” California Institute of Technology 16
1998
Earlier work this paper cites.
Masaki Oshikawa, “Commensurability, Excitation Gap, and Topology in Quantum Many-Particle Systems on a Periodic Lattice,” Phys. Rev. Lett. 84
2000
Earlier work this paper cites.
M. B. Hastings, “Lieb-Schultz-Mattis in higher dimensions,” Phys. Rev. B 69
2004
Earlier work this paper cites.
C. L. Kane and E. J. Mele, “Z 2
2005
Earlier work this paper cites.
Alexei Kitaev, “Anyons in an exactly solved model and beyond,” Annals of Physics 321
2006
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.
Tobias J. Osborne, “Simulating adiabatic evolution of gapped spin systems,” Phys. Rev. A 75
2007
Earlier work this paper cites.
Dominic V. Else, Ryan Thorngren, and T. Senthil, “Non-Fermi Liquids as Ersatz Fermi Liquids: General Constraints on Compressible Metals,” Physical Review X 11
Original
2007
Earlier work this paper cites.
Xiao-Liang Qi, Taylor L. Hughes, and Shou-Cheng Zhang, “Topological field theory of time-reversal invariant insulators,” Phys. Rev. B 78
Original
2008
Earlier work this paper cites.
Jeffrey C. Y. Teo, Liang Fu, and C. L. Kane, “Surface states and topological invariants in three-dimensional topological insulators: Application to bi 1 − x sb x {\text{bi}}_{1-x}{\text{sb}}_{x} ,” Phys. Rev. B 78
2008
Earlier work this paper cites.
M. Z. Hasan and C. L. Kane, “Colloquium: Topological insulators,” Reviews of Modern Physics 82
Original
2010
Earlier work this paper cites.
G. Rosenberg and M. Franz, “Witten effect in a crystalline topological insulator,” Phys. Rev. B 82
Original
2010
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
Original
2010
Earlier work this paper cites.
Alexander Altland and Ben D Simons, Condensed matter field theory (Cambridge university press, 2010)
2010
Earlier work this paper cites.
Matthew Yu, “Symmetries and anomalies of (1+1)d theories: 2-groups and symmetry fractionalization,” Journal of High Energy Physics 2021
Original
2010
Earlier work this paper cites.
Liang Fu, “Topological Crystalline Insulators,” Phys. Rev. Lett. 106
Original
2011
Earlier work this paper cites.

Similar

Ari M. Turner, Frank Pollmann, and Erez Berg, “Topological phases of one-dimensional fermions: An entanglement point of view,” Phys. Rev. B 83
Original
2011
Cited alongside, same era.
Lukasz Fidkowski and Alexei Kitaev, “Topological phases of fermions in one dimension,” Phys. Rev. B 83
Original
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
Original
2011
Cited alongside, same era.
Alexei Kitaev, “Toward topological classification of phases with short-range entanglement,” in Topological Insulators and Superconductors Workshop (Kavli Institute for Theoretical Physics, University of California, 2011)
2011
Cited alongside, same era.

Then

Hiroki Isobe and Liang Fu, “Theory of interacting topological crystalline insulators,” Phys. Rev. B 92
2015
Later among the works it cites.
Yohei Fuji, Frank Pollmann, and Masaki Oshikawa, “Distinct Trivial Phases Protected by a Point-Group Symmetry in Quantum Spin Chains,” Phys. Rev. Lett. 114
Original
2015
Later among the works it cites.
Meng Cheng, Michael Zaletel, Maissam Barkeshli, Ashvin Vishwanath, and Parsa Bonderson, “Translational Symmetry and Microscopic Constraints on Symmetry-Enriched Topological Phases: A View from the Surface,” Physical Review X 6
Original
2016
Later among the works it cites.
Edward Witten, “Fermion path integrals and topological phases,” Reviews of Modern Physics 88
Original
2016
Later among the works it cites.
Daniel S. Freed and Michael J. Hopkins, “Reflection positivity and invertible topological phases,” arXiv e-prints , arXiv:1604.06527 (2016), arXiv:1604.06527 [hep-th]

Beyond the bibliography

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2022

Average Symmetry-Protected Topological Phases

Ma, Ruochen, Wang, Chong

Understand

Symmetry-protected topological (SPT) phases are many-body quantum states that are topologically nontrivial as long as the relevant symmetries are unbroken.

In this work we show that SPT phases are also well defined for average symmetries, where quenched disorders locally break the symmetries, but restore the symmetries upon disorder averaging.
An example would be crystalline SPT phases with imperfect lattices.
Specifically, we define the notion of average SPT for disordered ensembles of quantum states.

Built on

Yang-Zhi Chou, Rahul M. Nandkishore, and Leo Radzihovsky, “Localized surfaces of three-dimensional topological insulators,” Phys. Rev. B 99
Original
1901
Earlier work this paper cites.
Itamar Kimchi, Yang-Zhi Chou, Rahul M. Nandkishore, and Leo Radzihovsky, “Anomalous localization at the boundary of an interacting topological insulator,” Phys. Rev. B 101
Original
1909
Earlier work this paper cites.
Elliott Lieb, Theodore Schultz, and Daniel Mattis, “Two soluble models of an antiferromagnetic chain,” Annals of Physics 16
1961
Earlier work this paper cites.
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.
Yoseph Imry and Shang-keng Ma, “Random-field instability of the ordered state of continuous symmetry,” Phys. Rev. Lett. 35
1975
Earlier work this paper cites.
Shang-keng Ma, Chandan Dasgupta, and Chin-kun Hu, “Random antiferromagnetic chain,” Physical review letters 43
1979
Earlier work this paper cites.
L. D. Landau and E. M. Lifshitz, Statistical Physics, Part 1 , Course of Theoretical Physics, Vol. 5 (Butterworth-Heinemann, Oxford, 1980)
1980
Earlier work this paper cites.
Chandan Dasgupta and Shang-keng Ma, “Low-temperature properties of the random heisenberg antiferromagnetic chain,” Physical review b 22
1980
Earlier work this paper cites.
D. J. Thouless, “Quantization of particle transport,” Phys. Rev. B 27
1983
Earlier work this paper cites.
P. A. Lee and A. Douglas Stone, “Universal conductance fluctuations in metals,” Phys. Rev. Lett. 55
1985
Earlier work this paper cites.
Steven R White, “Density matrix formulation for quantum renormalization groups,” Physical review letters 69
1992
Earlier work this paper cites.
Daniel S Fisher, “Random antiferromagnetic quantum spin chains,” Physical review b 50
1994
Earlier work this paper cites.
John Preskill, “Lecture notes for physics 229: Quantum information and computation,” California Institute of Technology 16
1998
Earlier work this paper cites.
Masaki Oshikawa, “Commensurability, Excitation Gap, and Topology in Quantum Many-Particle Systems on a Periodic Lattice,” Phys. Rev. Lett. 84
2000
Earlier work this paper cites.
M. B. Hastings, “Lieb-Schultz-Mattis in higher dimensions,” Phys. Rev. B 69
2004
Earlier work this paper cites.
C. L. Kane and E. J. Mele, “Z 2
2005
Earlier work this paper cites.
Alexei Kitaev, “Anyons in an exactly solved model and beyond,” Annals of Physics 321
2006
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.
Tobias J. Osborne, “Simulating adiabatic evolution of gapped spin systems,” Phys. Rev. A 75
2007
Earlier work this paper cites.
Dominic V. Else, Ryan Thorngren, and T. Senthil, “Non-Fermi Liquids as Ersatz Fermi Liquids: General Constraints on Compressible Metals,” Physical Review X 11
Original
2007
Earlier work this paper cites.
Xiao-Liang Qi, Taylor L. Hughes, and Shou-Cheng Zhang, “Topological field theory of time-reversal invariant insulators,” Phys. Rev. B 78
Original
2008
Earlier work this paper cites.
Jeffrey C. Y. Teo, Liang Fu, and C. L. Kane, “Surface states and topological invariants in three-dimensional topological insulators: Application to bi 1 − x sb x {\text{bi}}_{1-x}{\text{sb}}_{x} ,” Phys. Rev. B 78
2008
Earlier work this paper cites.
M. Z. Hasan and C. L. Kane, “Colloquium: Topological insulators,” Reviews of Modern Physics 82
Original
2010
Earlier work this paper cites.
G. Rosenberg and M. Franz, “Witten effect in a crystalline topological insulator,” Phys. Rev. B 82
Original
2010
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
Original
2010
Earlier work this paper cites.
Alexander Altland and Ben D Simons, Condensed matter field theory (Cambridge university press, 2010)
2010
Earlier work this paper cites.
Matthew Yu, “Symmetries and anomalies of (1+1)d theories: 2-groups and symmetry fractionalization,” Journal of High Energy Physics 2021
Original
2010
Earlier work this paper cites.
Liang Fu, “Topological Crystalline Insulators,” Phys. Rev. Lett. 106
Original
2011
Earlier work this paper cites.

Similar

Ari M. Turner, Frank Pollmann, and Erez Berg, “Topological phases of one-dimensional fermions: An entanglement point of view,” Phys. Rev. B 83
Original
2011
Cited alongside, same era.
Lukasz Fidkowski and Alexei Kitaev, “Topological phases of fermions in one dimension,” Phys. Rev. B 83
Original
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
Original
2011
Cited alongside, same era.
Alexei Kitaev, “Toward topological classification of phases with short-range entanglement,” in Topological Insulators and Superconductors Workshop (Kavli Institute for Theoretical Physics, University of California, 2011)
2011
Cited alongside, same era.

Then

Hiroki Isobe and Liang Fu, “Theory of interacting topological crystalline insulators,” Phys. Rev. B 92
2015
Later among the works it cites.
Yohei Fuji, Frank Pollmann, and Masaki Oshikawa, “Distinct Trivial Phases Protected by a Point-Group Symmetry in Quantum Spin Chains,” Phys. Rev. Lett. 114
Original
2015
Later among the works it cites.
Meng Cheng, Michael Zaletel, Maissam Barkeshli, Ashvin Vishwanath, and Parsa Bonderson, “Translational Symmetry and Microscopic Constraints on Symmetry-Enriched Topological Phases: A View from the Surface,” Physical Review X 6
Original
2016
Later among the works it cites.
Edward Witten, “Fermion path integrals and topological phases,” Reviews of Modern Physics 88
Original
2016
Later among the works it cites.
Daniel S. Freed and Michael J. Hopkins, “Reflection positivity and invertible topological phases,” arXiv e-prints , arXiv:1604.06527 (2016), arXiv:1604.06527 [hep-th]

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

Matthew B. Hastings, “Topological Order at Nonzero Temperature,” Phys. Rev. Lett. 107

Original

2011

Cited alongside, same era.

Ulrich Schollwöck, “The density-matrix renormalization group in the age of matrix product states,” Annals of Physics 326

Original

2011

Cited alongside, same era.

Frank Pollmann and Ari M. Turner, “Detection of symmetry-protected topological phases in one dimension,” Phys. Rev. B 86

Original

2012

Cited alongside, same era.

I. C. Fulga, B. van Heck, J. M. Edge, and A. R. Akhmerov, “Statistical Topological Insulators,” arXiv e-prints , arXiv:1212.6191 (2012), arXiv:1212.6191 [cond-mat.mes-hall]

Original

2012

Cited alongside, same era.

Zohar Ringel, Yaacov E. Kraus, and Ady Stern, “Strong side of weak topological insulators,” Phys. Rev. B 86

Original

2012

Cited alongside, same era.

Roger S. K. Mong, Jens H. Bardarson, and Joel E. Moore, “Quantum Transport and Two-Parameter Scaling at the Surface of a Weak Topological Insulator,” Phys. Rev. Lett. 108

Original

2012

Cited alongside, same era.

Liang Fu and C. L. Kane, “Topology, Delocalization via Average Symmetry and the Symplectic Anderson Transition,” Phys. Rev. Lett. 109

Original

2012

Cited alongside, same era.

Yang-Zhi Chou and Rahul M. Nandkishore, “Marginally localized edges of time-reversal symmetric topological superconductors,” Phys. Rev. B 103

Original

2012

Cited alongside, same era.

Original

2016