Built on

M. Barkeshli and M. Cheng, Relative anomalies in (2+1)d symmetry enriched topological states (2019), arXiv:1906.10691
Original
1906
Earlier work this paper cites.
X.-G. Wen, Quantum Field Theory of Many-Body Systems (Oxford Univ. Press, Oxford, 2004)
2004
Earlier work this paper cites.
P. H. Bonderson, Non-Abelian Anyons and Interferometry , Ph.D. thesis, California Institute of Technology (2007)
2007
Earlier work this paper cites.
N. Manjunath and M. Barkeshli, Classification of fractional quantum hall states with spatial symmetries (2020), arXiv:2012.11603 [cond-mat.str-el]
Original
2012
Earlier work this paper cites.
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
Earlier work this paper cites.
L. Fidkowski, X. Chen, and A. Vishwanath, Non-Abelian Topological Order on the Surface of a 3D Topological Superconductor from an Exactly Solved Model, Phys. Rev. X 3
Original
2013
Earlier work this paper cites.
A. M. Essin and M. Hermele, Spectroscopic signatures of crystal momentum fractionalization, Physical Review B 90
2014
Earlier work this paper cites.
A. Davydov, Bogomolov multiplier, double class-preserving automorphisms, and modular invariants for orbifolds, J. Math. Phys. 55
2014
Earlier work this paper cites.
M. Metlitski, L. Fidkowski, X. Chen, and A. Vishwanath, Interaction effects on 3D topological superconductors: surface topological order from vortex condensation, the 16 fold way and fermionic Kramers doublets (2014), arXiv:1406.3032
Original
2014
Earlier work this paper cites.

Similar

L. Fidkowski and A. Vishwanath, Realizing anomalous anyonic symmetries at the surfaces of 3d gauge theories (2015), arXiv:1511.01502
Original
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Cited alongside, same era.
M. Cheng, M. Zaletel, M. Barkeshli, A. Vishwanath, and P. Bonderson, Translational symmetry and microscopic constraints on symmetry-enriched topological phases: A view from the surface, Phys. Rev. X 6
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2017
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Y. Qi and M. Cheng, Classification of symmetry fractionalization in gapped z2 spin liquids, Physical Review B 97
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Then

Q.-R. Wang and Z.-C. Gu, Construction and Classification of Symmetry-Protected Topological Phases in Interacting Fermion Systems, Phys. Rev. X 10
2020
Later among the works it cites.
N. Manjunath and M. Barkeshli, Crystalline gauge fields and quantized discrete geometric response for abelian topological phases with lattice symmetry, Physical Review Research 3
2021
Closest in time.
S. Tata, R. Kobayashi, D. Bulmash, and M. Barkeshli, Anomalies in (2+1)D fermionic topological phases and (3+1)D path integral state sums for fermionic SPTs (2021), arXiv:2104.14567
Original
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Closest in time.
T. Johnson-Freyd and D. Reutter, Minimal nondegenerate extensions (2021), arXiv:2105.15167
Original
2021
Closest in time.
D. Delmastro, D. Gaiotto, and J. Gomis, Global anomalies on the hilbert space (2021), arXiv:2101.02218 [hep-th]

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2021

Fermionic symmetry fractionalization in (2+1)D

Bulmash, Daniel, Barkeshli, Maissam

Understand

We develop a systematic theory of symmetry fractionalization for fermionic topological phases of matter in (2+1)D with a general fermionic symmetry group $G_f$.

In general $G_f$ is a central extension of the bosonic symmetry group $G_b$ by fermion parity, $(-1)^F$, characterized by a non-trivial cohomology class $[\omega_2] \in \mathcal{H}^2(G_b, \mathbb{Z}_2)$.
We show how the presence of local fermions places a number of constraints on the algebraic data that defines the action of the symmetry on the super-modular tensor category that characterizes the anyon content.
We find two separate obstructions to defining symmetry fractionalization, which we refer to as the bosonic and fermionic symmetry localization obstructions.

Built on

M. Barkeshli and M. Cheng, Relative anomalies in (2+1)d symmetry enriched topological states (2019), arXiv:1906.10691
Original
1906
Earlier work this paper cites.
X.-G. Wen, Quantum Field Theory of Many-Body Systems (Oxford Univ. Press, Oxford, 2004)
2004
Earlier work this paper cites.
P. H. Bonderson, Non-Abelian Anyons and Interferometry , Ph.D. thesis, California Institute of Technology (2007)
2007
Earlier work this paper cites.
N. Manjunath and M. Barkeshli, Classification of fractional quantum hall states with spatial symmetries (2020), arXiv:2012.11603 [cond-mat.str-el]
Original
2012
Earlier work this paper cites.
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
Earlier work this paper cites.
L. Fidkowski, X. Chen, and A. Vishwanath, Non-Abelian Topological Order on the Surface of a 3D Topological Superconductor from an Exactly Solved Model, Phys. Rev. X 3
Original
2013
Earlier work this paper cites.
A. M. Essin and M. Hermele, Spectroscopic signatures of crystal momentum fractionalization, Physical Review B 90
2014
Earlier work this paper cites.
A. Davydov, Bogomolov multiplier, double class-preserving automorphisms, and modular invariants for orbifolds, J. Math. Phys. 55
2014
Earlier work this paper cites.
M. Metlitski, L. Fidkowski, X. Chen, and A. Vishwanath, Interaction effects on 3D topological superconductors: surface topological order from vortex condensation, the 16 fold way and fermionic Kramers doublets (2014), arXiv:1406.3032
Original
2014
Earlier work this paper cites.

Similar

L. Fidkowski and A. Vishwanath, Realizing anomalous anyonic symmetries at the surfaces of 3d gauge theories (2015), arXiv:1511.01502
Original
2015
Cited alongside, same era.
M. Cheng, M. Zaletel, M. Barkeshli, A. Vishwanath, and P. Bonderson, Translational symmetry and microscopic constraints on symmetry-enriched topological phases: A view from the surface, Phys. Rev. X 6
2016
Cited alongside, same era.
C. Galindo and C. Venegas-Ramírez, Categorical fermionic actions and minimal modular extensions (2017), arXiv:1712.07097
Original
2017
Cited alongside, same era.
Y. Qi and M. Cheng, Classification of symmetry fractionalization in gapped z2 spin liquids, Physical Review B 97
2018
Cited alongside, same era.
P. Bonderson, E. Rowell, Z. Wang, and Q. Zhang, Congruence subgroups and super-modular categories, Pacific Journal of Mathematics 296

Then

Q.-R. Wang and Z.-C. Gu, Construction and Classification of Symmetry-Protected Topological Phases in Interacting Fermion Systems, Phys. Rev. X 10
2020
Later among the works it cites.
N. Manjunath and M. Barkeshli, Crystalline gauge fields and quantized discrete geometric response for abelian topological phases with lattice symmetry, Physical Review Research 3
2021
Closest in time.
S. Tata, R. Kobayashi, D. Bulmash, and M. Barkeshli, Anomalies in (2+1)D fermionic topological phases and (3+1)D path integral state sums for fermionic SPTs (2021), arXiv:2104.14567
Original
2021
Closest in time.
T. Johnson-Freyd and D. Reutter, Minimal nondegenerate extensions (2021), arXiv:2105.15167
Original
2021
Closest in time.
D. Delmastro, D. Gaiotto, and J. Gomis, Global anomalies on the hilbert space (2021), arXiv:2101.02218 [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…

2018

Cited alongside, same era.

L. Fidkowski, A. Vishwanath, and M. A. Metlitski, Surface topological order and a new ’t hooft anomaly of interaction enabled 3+1d fermion spts (2018), arXiv:1804.08628 [cond-mat.str-el]

Original

2018

Cited alongside, same era.

M. Cheng, Fermionic lieb-schultz-mattis theorems and weak symmetry-protected phases, Phys. Rev. B 99

2019

Cited alongside, same era.

F. Benini, C. Córdova, and P.-S. Hsin, On 2-group global symmetries and their anomalies, Journal of High Energy Physics 2019

2019

Cited alongside, same era.

D. Bulmash and M. Barkeshli, Absolute anomalies in (2+1)d symmetry-enriched topological states and exact (3+1)d constructions, Phys. Rev. Research 2

2020

Cited alongside, same era.

M. Barkeshli, P. Bonderson, M. Cheng, and Z. Wang, Symmetry fractionalization, defects, and gauging of topological phases, Phys. Rev. B 100

Original

Cited in the paper.

M. Barkeshli, P. Bonderson, M. Cheng, C.-M. Jian, and K. Walker, Reflection and time reversal symmetry enriched topological phases of matter: Path integrals, non-orientable manifolds, and anomalies, Communications in Mathematical Physics 10.1007/s00220-019-03475-8 (2019b), arXiv:1612.07792

Original

Cited in the paper.

P. Bruillard, C. Galindo, T. Hagge, S.-H. Ng, J. Y. Plavnik, E. C. Rowell, and Z. Wang, Fermionic modular categories and the 16-fold way, Journal of Mathematical Physics 58

Cited in the paper.

Original

2021

Closest in time.

D. Bulmash and M. Barkeshli, Anomaly cascade in (2+1)D fermionic topological phases (2021), arXiv:2109.10922

Original

2021

Closest in time.

D. Aasen, P. Bonderson, and C. Knapp, Characterization and Classification of Fermionic Symmetry Enriched Topological Phases (2021), arXiv:2109.10911

Original

2021

Closest in time.

M. Barkeshli, Y.-A. Chen, P.-S. Hsin, and N. Manjunath, Classification of (2+1)d invertible fermionic topological phases with symmetry (2021), arXiv:2109.11039

Original

2021

Closest in time.