Built on

D. S. Freed and M. J. Hopkins, “Invertible phases of matter with spatial symmetry,” arXiv:1901.06419 [math-ph]
Original
1901
Earlier work this paper cites.
A. Karch, D. Tong, and C. Turner, “A Web of 2d Dualities: 𝐙 2 {\bf Z}_{2} Gauge Fields and Arf Invariants,” SciPost Phys
Original
1902
Earlier work this paper cites.
L. Fidkowski, J. Haah, M. B. Hastings, and N. Tantivasadakarn, “Disentangling the Generalized Double Semion Model,” arXiv:1906.04188 [math-ph]
Original
1906
Earlier work this paper cites.
L. Tsui and X.-G. Wen, “Lattice models that realize Z n Z_{n} -1 symmetry-protected topological states for even n n ,” Phys. Rev. B
Original
1908
Earlier work this paper cites.
P.-S. Hsin and S.-H. Shao, “Lorentz Symmetry Fractionalization and Dualities in (2+1)d,” SciPost Phys
Original
1909
Earlier work this paper cites.
W. Ji, S.-H. Shao, and X.-G. Wen, “Topological Transition on the Conformal Manifold,” Phys. Rev. Res
Original
1909
Earlier work this paper cites.
J. Ang, K. Roumpedakis, and S. Seifnashri, “Line Operators of Gauge Theories on Non-Spin Manifolds,” JHEP
Original
1911
Earlier work this paper cites.
W.-T. Wu, “On Pontrjagin classes III,” Acta Math. Sinica
1954
Earlier work this paper cites.
E. Thomas, “On the cohomology of the real grassmann complexes and the characteristic classes of n-plane bundles,” Transactions of the American Mathematical Society
1960
Earlier work this paper cites.
W. Browder, “The Kervaire Invariant of Framed Manifolds and its Generalization,” Annals of Mathematics
1969
Earlier work this paper cites.
S. Morita, “On the Pontrjagin Square and the Signature,” Journal of the Faculty of Science, the University of Tokyo. Sect. 1 A, Mathematics
1971
Earlier work this paper cites.
E. H. Brown, “Generalizations of the Kervaire Invariant,” Annals of Mathematics
1972
Earlier work this paper cites.
Annals of mathematics studies. Princeton University Press, 1974
J. Milnor, J. Stasheff, J. Stasheff, and P. University, Characteristic Classes · 1974
Earlier work this paper cites.
S. R. Coleman, “More About the Massive Schwinger Model,” Annals Phys
1976
Earlier work this paper cites.
P. Goddard, J. Nuyts, and D. I. Olive, “Gauge Theories and Magnetic Charge,” Nucl. Phys. B
1977
Earlier work this paper cites.
E. Witten, “Dyons of Charge e theta/2 pi,” Phys. Lett. B
1979
Earlier work this paper cites.
Graduate Texts in Mathematics. Springer, 1982
K. Brown, Cohomology of Groups · 1982
Earlier work this paper cites.
F. Wilczek, “Magnetic Flux, Angular Momentum, and Statistics,” Phys. Rev. Lett
1982
Earlier work this paper cites.
F. Haldane, “Continuum dynamics of the 1-D Heisenberg antiferromagnetic identification with the O(3) nonlinear sigma model,” Phys. Lett. A
1983
Earlier work this paper cites.
A. S. Goldhaber, R. MacKenzie, and F. Wilczek, “Field corrections to induced statistics,” Mod. Phys. Lett
1989
Earlier work this paper cites.
R. Dijkgraaf and E. Witten, “Topological Gauge Theories and Group Cohomology,” Commun. Math. Phys
1990
Earlier work this paper cites.

Similar

London Mathematical Society Lecture Note Series. Cambridge University Press, 1994
J. A. Hillman, The Algebraic Characterization of Geometric 4-Manifolds · 1994
Cited alongside, same era.
D. S. Freed and E. Witten, “Anomalies in string theory with D-branes,” Asian J. Math
1999
Cited alongside, same era.
A. Y. Kitaev, “Unpaired Majorana fermions in quantum wires,” Phys. Usp
2001
Cited alongside, same era.
A. Cappelli, M. Huerta, and G. R. Zemba, “Thermal transport in chiral conformal theories and hierarchical quantum Hall states,” Nucl. Phys. B
2002
Cited alongside, same era.
V. Borokhov, A. Kapustin, and X.-k. Wu, “Topological disorder operators in three-dimensional conformal field theory,” JHEP
2002
Cited alongside, same era.
A. Y. Kitaev, “Fault tolerant quantum computation by anyons,” Annals Phys

Then

C. von Keyserlingk, F. Burnell, and S. H. Simon, “Three-dimensional topological lattice models with surface anyons,” Phys. Rev. B
Original
2013
Later among the works it cites.
D. V. Else and C. Nayak, “Classifying symmetry-protected topological phases through the anomalous action of the symmetry on the edge,” Phys. Rev. B
Original
2014
Later among the works it cites.
A. Kapustin and N. Seiberg, “Coupling a QFT to a TQFT and Duality,” JHEP
Original
2014
Later among the works it cites.
T. Senthil, “Symmetry-protected topological phases of quantum matter,” Annual Review of Condensed Matter Physics
2015
Later among the works it cites.
D. Gaiotto, A. Kapustin, N. Seiberg, and B. Willett, “Generalized Global Symmetries,” JHEP
Original

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2021

Exotic Invertible Phases with Higher-Group Symmetries

Hsin, Po-Shen, Ji, Wenjie, Jian, Chao-Ming

Understand

We investigate a family of invertible phases of matter with higher-dimensional exotic excitations in even spacetime dimensions, which includes and generalizes the Kitaev's chain in 1+1d.

The excitation has $\mathbb{Z}_2$ higher-form symmetry that mixes with the spacetime Lorentz symmetry to form a higher group spacetime symmetry.
We focus on the invertible exotic loop topological phase in 3+1d.
This invertible phase is protected by the $\mathbb{Z}_2$ one-form symmetry and the time-reversal symmetry, and has surface thermal Hall conductance not realized in conventional time-reversal symmetric ordinary bosonic systems without local fermion particles and the exotic loops.

Built on

D. S. Freed and M. J. Hopkins, “Invertible phases of matter with spatial symmetry,” arXiv:1901.06419 [math-ph]
Original
1901
Earlier work this paper cites.
A. Karch, D. Tong, and C. Turner, “A Web of 2d Dualities: 𝐙 2 {\bf Z}_{2} Gauge Fields and Arf Invariants,” SciPost Phys
Original
1902
Earlier work this paper cites.
L. Fidkowski, J. Haah, M. B. Hastings, and N. Tantivasadakarn, “Disentangling the Generalized Double Semion Model,” arXiv:1906.04188 [math-ph]
Original
1906
Earlier work this paper cites.
L. Tsui and X.-G. Wen, “Lattice models that realize Z n Z_{n} -1 symmetry-protected topological states for even n n ,” Phys. Rev. B
Original
1908
Earlier work this paper cites.
P.-S. Hsin and S.-H. Shao, “Lorentz Symmetry Fractionalization and Dualities in (2+1)d,” SciPost Phys
Original
1909
Earlier work this paper cites.
W. Ji, S.-H. Shao, and X.-G. Wen, “Topological Transition on the Conformal Manifold,” Phys. Rev. Res
Original
1909
Earlier work this paper cites.
J. Ang, K. Roumpedakis, and S. Seifnashri, “Line Operators of Gauge Theories on Non-Spin Manifolds,” JHEP
Original
1911
Earlier work this paper cites.
W.-T. Wu, “On Pontrjagin classes III,” Acta Math. Sinica
1954
Earlier work this paper cites.
E. Thomas, “On the cohomology of the real grassmann complexes and the characteristic classes of n-plane bundles,” Transactions of the American Mathematical Society
1960
Earlier work this paper cites.
W. Browder, “The Kervaire Invariant of Framed Manifolds and its Generalization,” Annals of Mathematics
1969
Earlier work this paper cites.
S. Morita, “On the Pontrjagin Square and the Signature,” Journal of the Faculty of Science, the University of Tokyo. Sect. 1 A, Mathematics
1971
Earlier work this paper cites.
E. H. Brown, “Generalizations of the Kervaire Invariant,” Annals of Mathematics
1972
Earlier work this paper cites.
Annals of mathematics studies. Princeton University Press, 1974
J. Milnor, J. Stasheff, J. Stasheff, and P. University, Characteristic Classes · 1974
Earlier work this paper cites.
S. R. Coleman, “More About the Massive Schwinger Model,” Annals Phys
1976
Earlier work this paper cites.
P. Goddard, J. Nuyts, and D. I. Olive, “Gauge Theories and Magnetic Charge,” Nucl. Phys. B
1977
Earlier work this paper cites.
E. Witten, “Dyons of Charge e theta/2 pi,” Phys. Lett. B
1979
Earlier work this paper cites.
Graduate Texts in Mathematics. Springer, 1982
K. Brown, Cohomology of Groups · 1982
Earlier work this paper cites.
F. Wilczek, “Magnetic Flux, Angular Momentum, and Statistics,” Phys. Rev. Lett
1982
Earlier work this paper cites.
F. Haldane, “Continuum dynamics of the 1-D Heisenberg antiferromagnetic identification with the O(3) nonlinear sigma model,” Phys. Lett. A
1983
Earlier work this paper cites.
A. S. Goldhaber, R. MacKenzie, and F. Wilczek, “Field corrections to induced statistics,” Mod. Phys. Lett
1989
Earlier work this paper cites.
R. Dijkgraaf and E. Witten, “Topological Gauge Theories and Group Cohomology,” Commun. Math. Phys
1990
Earlier work this paper cites.

Similar

London Mathematical Society Lecture Note Series. Cambridge University Press, 1994
J. A. Hillman, The Algebraic Characterization of Geometric 4-Manifolds · 1994
Cited alongside, same era.
D. S. Freed and E. Witten, “Anomalies in string theory with D-branes,” Asian J. Math
1999
Cited alongside, same era.
A. Y. Kitaev, “Unpaired Majorana fermions in quantum wires,” Phys. Usp
2001
Cited alongside, same era.
A. Cappelli, M. Huerta, and G. R. Zemba, “Thermal transport in chiral conformal theories and hierarchical quantum Hall states,” Nucl. Phys. B
2002
Cited alongside, same era.
V. Borokhov, A. Kapustin, and X.-k. Wu, “Topological disorder operators in three-dimensional conformal field theory,” JHEP
2002
Cited alongside, same era.
A. Y. Kitaev, “Fault tolerant quantum computation by anyons,” Annals Phys

Then

C. von Keyserlingk, F. Burnell, and S. H. Simon, “Three-dimensional topological lattice models with surface anyons,” Phys. Rev. B
Original
2013
Later among the works it cites.
D. V. Else and C. Nayak, “Classifying symmetry-protected topological phases through the anomalous action of the symmetry on the edge,” Phys. Rev. B
Original
2014
Later among the works it cites.
A. Kapustin and N. Seiberg, “Coupling a QFT to a TQFT and Duality,” JHEP
Original
2014
Later among the works it cites.
T. Senthil, “Symmetry-protected topological phases of quantum matter,” Annual Review of Condensed Matter Physics
2015
Later among the works it cites.
D. Gaiotto, A. Kapustin, N. Seiberg, and B. Willett, “Generalized Global Symmetries,” JHEP
Original

Beyond the bibliography

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

Open on alphaXiv

alphaXiv is searching for related work…

2003

Cited alongside, same era.

D. S. Freed and G. W. Moore, “Setting the quantum integrand of M-theory,” Commun. Math. Phys

2006

Cited alongside, same era.

J. Elgueta, “Representation theory of 2-groups on kapranov and voevodsky’s 2-vector spaces,” Advances in Mathematics

2007

Cited alongside, same era.

A. Kitaev, “Periodic table for topological insulators and superconductors,” AIP Conf. Proc

Original

2009

Cited alongside, same era.

L. Bhardwaj, Y. Lee, and Y. Tachikawa, “ S L ( 2 , ℤ ) SL(2,\mathbb{Z}) action on QFTs with ℤ 2 \mathbb{Z}_{2} symmetry and the Brown-Kervaire invariants,” arXiv:2009.10099 [hep-th]

Original

2009

Cited alongside, same era.

M. Qi, L. Radzihovsky, and M. Hermele, “Fracton phases via exotic higher-form symmetry-breaking,” arXiv:2010.02254 [cond-mat.str-el]

Original

2010

Cited alongside, same era.

S. Gukov, P.-S. Hsin, and D. Pei, “Generalized Global Symmetries of T ⁡ [ M ] T[M] Theories. I,” arXiv:2010.15890 [hep-th]

Original

2010

Cited alongside, same era.

2015