Built on

B. J. Brown and D. J. Williamson, “Parallelized quantum error correction with fracton topological codes,” Phys. Rev. Res
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.
Z. Wan, J. Wang, and Y. Zheng, “Quantum 4d Yang-Mills Theory and Time-Reversal Symmetric 5d Higher-Gauge Topological Field Theory,” Phys. Rev. D
Original
1904
Earlier work this paper cites.
Y.-H. Lin and S.-H. Shao, “Anomalies and Bounds on Charged Operators,” Phys. Rev. D
Original
1904
Earlier work this paper cites.
W. Ji and X.-G. Wen, “Non-invertible anomalies and mapping-class-group transformation of anomalous partition functions,” Phys. Rev. Research
Original
1905
Earlier work this paper cites.
R. Verresen, R. Thorngren, N. G. Jones, and F. Pollmann, “Gapless Topological Phases and Symmetry-Enriched Quantum Criticality,” Phys. Rev. X
Original
1905
Earlier work this paper cites.
Z. Weinstein, G. Ortiz, and Z. Nussinov, “Universality Classes of Stabilizer Code Hamiltonians,” Phys. Rev. Lett
Original
1907
Earlier work this paper cites.
J. P. Ibieta-Jimenez, L. N. Q. Xavier, M. Petrucci, and P. Teotonio-Sobrinho, “Fractonlike phases from subsystem symmetries,” 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.
N. Seiberg, “Field Theories With a Vector Global Symmetry,” 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.
C. Córdova and K. Ohmori, “Anomaly Obstructions to Symmetry Preserving Gapped Phases,” arXiv:1910.04962 [hep-th]
Original
1910
Earlier work this paper cites.
J. Wang, Y.-Z. You, and Y. Zheng, “Gauge enhanced quantum criticality and time reversal deconfined domain wall: SU(2) Yang-Mills dynamics with topological terms,” Phys. Rev. Res
Original
1910
Earlier work this paper cites.
T. Devakul, W. Shirley, and J. Wang, “Strong planar subsystem symmetry-protected topological phases and their dual fracton orders,” Phys. Rev. Res
Original
1910
Earlier work this paper cites.
Z. Wan, J. Wang, and Y. Zheng, “Higher anomalies, higher symmetries, and cobordisms II: Lorentz symmetry extension and enriched bosonic / fermionic quantum gauge theory,” Ann. Math. Sci. Appl
Original
1912
Earlier work this paper cites.
Z. Wan and J. Wang, “Higher anomalies, higher symmetries, and cobordisms III: QCD matter phases anew,” Nucl. Phys. B
Original
1912
Earlier work this paper cites.
R. Thorngren and Y. Wang, “Fusion Category Symmetry I: Anomaly In-Flow and Gapped Phases,” arXiv:1912.02817 [hep-th]
Original
1912
Earlier work this paper cites.
W. Ji and X.-G. Wen, “Categorical symmetry and noninvertible anomaly in symmetry-breaking and topological phase transitions,” Phys. Rev. Res
Original
1912
Earlier work this paper cites.
J. Haah, “Local stabilizer codes in three dimensions without string logical operators,” Phys. Rev. A
Original
1962
Earlier work this paper cites.
T. Kennedy and H. Tasaki, “Hidden symmetry breaking and the Haldane phase in S=1 quantum spin chains,” Communications in Mathematical Physics
1992
Earlier work this paper cites.
T. Kennedy and H. Tasaki, “Hidden ℤ 2 × ℤ 2 \mathbb{Z}_{2}\times\mathbb{Z}_{2} symmetry breaking in haldane-gap antiferromagnets,” Phys. Rev. B
1992
Earlier work this paper cites.
M. Oshikawa, “Hidden ℤ 2 × ℤ 2 \mathbb{Z}_{2}\times\mathbb{Z}_{2} symmetry in quantum spin chains with arbitrary integer spin,” Journal of Physics: Condensed Matter
1992
Earlier work this paper cites.
A. Paramekanti, L. Balents, and M. P. Fisher, “Ring exchange, the exciton Bose liquid, and bosonization in two dimensions,” Phys. Rev. B
2002
Earlier work this paper cites.
N. Tantivasadakarn, “Jordan-Wigner Dualities for Translation-Invariant Hamiltonians in Any Dimension: Emergent Fermions in Fracton Topological Order,” Phys. Rev. Res
Original
2002
Earlier work this paper cites.
C.-T. Hsieh, Y. Nakayama, and Y. Tachikawa, “Fermionic minimal models,” Phys. Rev. Lett
Original
2002
Earlier work this paper cites.
N. Seiberg and S.-H. Shao, “Exotic Symmetries, Duality, and Fractons in 2+1-Dimensional Quantum Field Theory,” SciPost Phys
Original
2003
Earlier work this paper cites.
J. Frohlich, J. Fuchs, I. Runkel, and C. Schweigert, “Kramers-Wannier duality from conformal defects,” Phys. Rev. Lett
2004
Earlier work this paper cites.
N. Seiberg and S.-H. Shao, “Exotic U ⁡ ( 1 ) U(1) Symmetries, Duality, and Fractons in 3+1-Dimensional Quantum Field Theory,” SciPost Phys
Original
2004
Earlier work this paper cites.
N. Seiberg and S.-H. Shao, “Exotic ℤ N \mathbb{Z}_{N} symmetries, duality, and fractons in 3+1-dimensional quantum field theory,” SciPost Phys
Original
2004
Earlier work this paper cites.
J. E. Moore and D.-H. Lee, “Geometric effects on t-breaking in p + i p p+ip and d + i d d+id superconducting arrays,” Phys. Rev. B
2004
Earlier work this paper cites.
C. Xu and J. E. Moore, “Strong-weak coupling self-duality in the two-dimensional quantum phase transition of p + i p p+ip superconducting arrays,” Phys. Rev. Lett
2004
Earlier work this paper cites.
D. R. Morrison, S. Schafer-Nameki, and B. Willett, “Higher-Form Symmetries in 5d,” JHEP
Original
2005
Earlier work this paper cites.
C. D. Batista and Z. Nussinov, “Generalized Elitzur’s theorem and dimensional reduction,” Phys. Rev. B
2005
Earlier work this paper cites.
L. Kong, T. Lan, X.-G. Wen, Z.-H. Zhang, and H. Zheng, “Algebraic higher symmetry and categorical symmetry – a holographic and entanglement view of symmetry,” Phys. Rev. Res
Original
2005
Earlier work this paper cites.
C. Xu and J. Moore, “Reduction of effective dimensionality in lattice models of superconducting arrays and frustrated magnets,” Nuclear Physics B
2005
Earlier work this paper cites.
J. Frohlich, J. Fuchs, I. Runkel, and C. Schweigert, “Duality and defects in rational conformal field theory,” Nucl. Phys. B
2007
Earlier work this paper cites.
P. Gorantla, H. T. Lam, N. Seiberg, and S.-H. Shao, “More Exotic Field Theories in 3+1 Dimensions,” SciPost Phys
Original
2007
Earlier work this paper cites.
L. Bhardwaj and S. Schäfer-Nameki, “Higher-form symmetries of 6d and 5d theories,” JHEP
Original
2008
Earlier work this paper cites.
Z. Komargodski, K. Ohmori, K. Roumpedakis, and S. Seifnashri, “Symmetries and strings of adjoint QCD 2
Original
2008
Earlier work this paper cites.
D. Aasen, P. Fendley, and R. S. K. Mong, “Topological Defects on the Lattice: Dualities and Degeneracies,” arXiv:2008.08598 [cond-mat.stat-mech]
Original
2008
Earlier work this paper cites.
R. Thorngren, A. Vishwanath, and R. Verresen, “Intrinsically Gapless Topological Phases,” arXiv:2008.06638 [cond-mat.str-el]
Original
2008
Earlier work this paper cites.
Z. Nussinov and G. Ortiz, “Sufficient symmetry conditions for Topological Quantum Order,” Proc. Nat. Acad. Sci
2009
Earlier work this paper cites.
Z. Nussinov and G. Ortiz, “A symmetry principle for topological quantum order,” Annals Phys
2009
Earlier work this paper cites.
R. Orús, A. C. Doherty, and G. Vidal, “First order phase transition in the anisotropic quantum orbital compass model,” Phys. Rev. Lett
2009
Earlier work this paper cites.

Similar

A. Karch and A. Raz, “Reduced Conformal Symmetry,” JHEP
Original
2009
Cited alongside, same era.
T. Devakul and D. J. Williamson, “Fractalizing quantum codes,” Quantum
Original
2009
Cited alongside, same era.
M. Qi, L. Radzihovsky, and M. Hermele, “Fracton phases via exotic higher-form symmetry-breaking,” Annals Phys
Original
2010
Cited alongside, same era.
P. Gorantla, H. T. Lam, N. Seiberg, and S.-H. Shao, “fcc lattice, checkerboards, fractons, and quantum field theory,” Phys. Rev. B
Original
2010
Cited alongside, same era.
E. Cobanera, G. Ortiz, and Z. Nussinov, “The Bond-Algebraic Approach to Dualities,” Adv. Phys
Original

Then

Z. Weinstein, E. Cobanera, G. Ortiz, and Z. Nussinov, “Absence of finite temperature phase transitions in the X-Cube model and its ℤ p \mathbb{Z}_{p} generalization,” Annals Phys
Original
2020
Later among the works it cites.
L. Bhardwaj, M. Hubner, and S. Schafer-Nameki, “1-form Symmetries of 4d N=2 Class S Theories,” SciPost Phys
Original
2021
Later among the works it cites.
M. M. Anber and E. Poppitz, “Nonperturbative effects in the Standard Model with gauged 1-form symmetry,” JHEP
Original
2021
Later among the works it cites.
T.-C. Huang, Y.-H. Lin, and S. Seifnashri, “Construction of two-dimensional topological field theories with non-invertible symmetries,” JHEP
Original
2021
Later among the works it cites.
M. Nguyen, Y. Tanizaki, and M. Ünsal, “Semi-Abelian gauge theories, non-invertible symmetries, and string tensions beyond N N -ality,” JHEP

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2023

Subsystem Non-Invertible Symmetry Operators and Defects

Cao, Weiguang, Li, Linhao, Yamazaki, Masahito et al.

Understand

We explore non-invertible symmetries in two-dimensional lattice models with subsystem $\mathbb Z_2$ symmetry.

We introduce a subsystem $\mathbb Z_2$-gauging procedure, called the subsystem Kramers-Wannier transformation, which generalizes the ordinary Kramers-Wannier transformation.
The corresponding duality operators and defects are constructed by gaugings on the whole or half of the Hilbert space.
By gauging twice, we derive fusion rules of duality operators and defects, which enriches ordinary Ising fusion rules with subsystem features.

Built on

B. J. Brown and D. J. Williamson, “Parallelized quantum error correction with fracton topological codes,” Phys. Rev. Res
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.
Z. Wan, J. Wang, and Y. Zheng, “Quantum 4d Yang-Mills Theory and Time-Reversal Symmetric 5d Higher-Gauge Topological Field Theory,” Phys. Rev. D
Original
1904
Earlier work this paper cites.
Y.-H. Lin and S.-H. Shao, “Anomalies and Bounds on Charged Operators,” Phys. Rev. D
Original
1904
Earlier work this paper cites.
W. Ji and X.-G. Wen, “Non-invertible anomalies and mapping-class-group transformation of anomalous partition functions,” Phys. Rev. Research
Original
1905
Earlier work this paper cites.
R. Verresen, R. Thorngren, N. G. Jones, and F. Pollmann, “Gapless Topological Phases and Symmetry-Enriched Quantum Criticality,” Phys. Rev. X
Original
1905
Earlier work this paper cites.
Z. Weinstein, G. Ortiz, and Z. Nussinov, “Universality Classes of Stabilizer Code Hamiltonians,” Phys. Rev. Lett
Original
1907
Earlier work this paper cites.
J. P. Ibieta-Jimenez, L. N. Q. Xavier, M. Petrucci, and P. Teotonio-Sobrinho, “Fractonlike phases from subsystem symmetries,” 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.
N. Seiberg, “Field Theories With a Vector Global Symmetry,” 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.
C. Córdova and K. Ohmori, “Anomaly Obstructions to Symmetry Preserving Gapped Phases,” arXiv:1910.04962 [hep-th]
Original
1910
Earlier work this paper cites.
J. Wang, Y.-Z. You, and Y. Zheng, “Gauge enhanced quantum criticality and time reversal deconfined domain wall: SU(2) Yang-Mills dynamics with topological terms,” Phys. Rev. Res
Original
1910
Earlier work this paper cites.
T. Devakul, W. Shirley, and J. Wang, “Strong planar subsystem symmetry-protected topological phases and their dual fracton orders,” Phys. Rev. Res
Original
1910
Earlier work this paper cites.
Z. Wan, J. Wang, and Y. Zheng, “Higher anomalies, higher symmetries, and cobordisms II: Lorentz symmetry extension and enriched bosonic / fermionic quantum gauge theory,” Ann. Math. Sci. Appl
Original
1912
Earlier work this paper cites.
Z. Wan and J. Wang, “Higher anomalies, higher symmetries, and cobordisms III: QCD matter phases anew,” Nucl. Phys. B
Original
1912
Earlier work this paper cites.
R. Thorngren and Y. Wang, “Fusion Category Symmetry I: Anomaly In-Flow and Gapped Phases,” arXiv:1912.02817 [hep-th]
Original
1912
Earlier work this paper cites.
W. Ji and X.-G. Wen, “Categorical symmetry and noninvertible anomaly in symmetry-breaking and topological phase transitions,” Phys. Rev. Res
Original
1912
Earlier work this paper cites.
J. Haah, “Local stabilizer codes in three dimensions without string logical operators,” Phys. Rev. A
Original
1962
Earlier work this paper cites.
T. Kennedy and H. Tasaki, “Hidden symmetry breaking and the Haldane phase in S=1 quantum spin chains,” Communications in Mathematical Physics
1992
Earlier work this paper cites.
T. Kennedy and H. Tasaki, “Hidden ℤ 2 × ℤ 2 \mathbb{Z}_{2}\times\mathbb{Z}_{2} symmetry breaking in haldane-gap antiferromagnets,” Phys. Rev. B
1992
Earlier work this paper cites.
M. Oshikawa, “Hidden ℤ 2 × ℤ 2 \mathbb{Z}_{2}\times\mathbb{Z}_{2} symmetry in quantum spin chains with arbitrary integer spin,” Journal of Physics: Condensed Matter
1992
Earlier work this paper cites.
A. Paramekanti, L. Balents, and M. P. Fisher, “Ring exchange, the exciton Bose liquid, and bosonization in two dimensions,” Phys. Rev. B
2002
Earlier work this paper cites.
N. Tantivasadakarn, “Jordan-Wigner Dualities for Translation-Invariant Hamiltonians in Any Dimension: Emergent Fermions in Fracton Topological Order,” Phys. Rev. Res
Original
2002
Earlier work this paper cites.
C.-T. Hsieh, Y. Nakayama, and Y. Tachikawa, “Fermionic minimal models,” Phys. Rev. Lett
Original
2002
Earlier work this paper cites.
N. Seiberg and S.-H. Shao, “Exotic Symmetries, Duality, and Fractons in 2+1-Dimensional Quantum Field Theory,” SciPost Phys
Original
2003
Earlier work this paper cites.
J. Frohlich, J. Fuchs, I. Runkel, and C. Schweigert, “Kramers-Wannier duality from conformal defects,” Phys. Rev. Lett
2004
Earlier work this paper cites.
N. Seiberg and S.-H. Shao, “Exotic U ⁡ ( 1 ) U(1) Symmetries, Duality, and Fractons in 3+1-Dimensional Quantum Field Theory,” SciPost Phys
Original
2004
Earlier work this paper cites.
N. Seiberg and S.-H. Shao, “Exotic ℤ N \mathbb{Z}_{N} symmetries, duality, and fractons in 3+1-dimensional quantum field theory,” SciPost Phys
Original
2004
Earlier work this paper cites.
J. E. Moore and D.-H. Lee, “Geometric effects on t-breaking in p + i p p+ip and d + i d d+id superconducting arrays,” Phys. Rev. B
2004
Earlier work this paper cites.
C. Xu and J. E. Moore, “Strong-weak coupling self-duality in the two-dimensional quantum phase transition of p + i p p+ip superconducting arrays,” Phys. Rev. Lett
2004
Earlier work this paper cites.
D. R. Morrison, S. Schafer-Nameki, and B. Willett, “Higher-Form Symmetries in 5d,” JHEP
Original
2005
Earlier work this paper cites.
C. D. Batista and Z. Nussinov, “Generalized Elitzur’s theorem and dimensional reduction,” Phys. Rev. B
2005
Earlier work this paper cites.
L. Kong, T. Lan, X.-G. Wen, Z.-H. Zhang, and H. Zheng, “Algebraic higher symmetry and categorical symmetry – a holographic and entanglement view of symmetry,” Phys. Rev. Res
Original
2005
Earlier work this paper cites.
C. Xu and J. Moore, “Reduction of effective dimensionality in lattice models of superconducting arrays and frustrated magnets,” Nuclear Physics B
2005
Earlier work this paper cites.
J. Frohlich, J. Fuchs, I. Runkel, and C. Schweigert, “Duality and defects in rational conformal field theory,” Nucl. Phys. B
2007
Earlier work this paper cites.
P. Gorantla, H. T. Lam, N. Seiberg, and S.-H. Shao, “More Exotic Field Theories in 3+1 Dimensions,” SciPost Phys
Original
2007
Earlier work this paper cites.
L. Bhardwaj and S. Schäfer-Nameki, “Higher-form symmetries of 6d and 5d theories,” JHEP
Original
2008
Earlier work this paper cites.
Z. Komargodski, K. Ohmori, K. Roumpedakis, and S. Seifnashri, “Symmetries and strings of adjoint QCD 2
Original
2008
Earlier work this paper cites.
D. Aasen, P. Fendley, and R. S. K. Mong, “Topological Defects on the Lattice: Dualities and Degeneracies,” arXiv:2008.08598 [cond-mat.stat-mech]
Original
2008
Earlier work this paper cites.
R. Thorngren, A. Vishwanath, and R. Verresen, “Intrinsically Gapless Topological Phases,” arXiv:2008.06638 [cond-mat.str-el]
Original
2008
Earlier work this paper cites.
Z. Nussinov and G. Ortiz, “Sufficient symmetry conditions for Topological Quantum Order,” Proc. Nat. Acad. Sci
2009
Earlier work this paper cites.
Z. Nussinov and G. Ortiz, “A symmetry principle for topological quantum order,” Annals Phys
2009
Earlier work this paper cites.
R. Orús, A. C. Doherty, and G. Vidal, “First order phase transition in the anisotropic quantum orbital compass model,” Phys. Rev. Lett
2009
Earlier work this paper cites.

Similar

A. Karch and A. Raz, “Reduced Conformal Symmetry,” JHEP
Original
2009
Cited alongside, same era.
T. Devakul and D. J. Williamson, “Fractalizing quantum codes,” Quantum
Original
2009
Cited alongside, same era.
M. Qi, L. Radzihovsky, and M. Hermele, “Fracton phases via exotic higher-form symmetry-breaking,” Annals Phys
Original
2010
Cited alongside, same era.
P. Gorantla, H. T. Lam, N. Seiberg, and S.-H. Shao, “fcc lattice, checkerboards, fractons, and quantum field theory,” Phys. Rev. B
Original
2010
Cited alongside, same era.
E. Cobanera, G. Ortiz, and Z. Nussinov, “The Bond-Algebraic Approach to Dualities,” Adv. Phys
Original

Then

Z. Weinstein, E. Cobanera, G. Ortiz, and Z. Nussinov, “Absence of finite temperature phase transitions in the X-Cube model and its ℤ p \mathbb{Z}_{p} generalization,” Annals Phys
Original
2020
Later among the works it cites.
L. Bhardwaj, M. Hubner, and S. Schafer-Nameki, “1-form Symmetries of 4d N=2 Class S Theories,” SciPost Phys
Original
2021
Later among the works it cites.
M. M. Anber and E. Poppitz, “Nonperturbative effects in the Standard Model with gauged 1-form symmetry,” JHEP
Original
2021
Later among the works it cites.
T.-C. Huang, Y.-H. Lin, and S. Seifnashri, “Construction of two-dimensional topological field theories with non-invertible symmetries,” JHEP
Original
2021
Later among the works it cites.
M. Nguyen, Y. Tanizaki, and M. Ünsal, “Semi-Abelian gauge theories, non-invertible symmetries, and string tensions beyond N N -ality,” JHEP

Beyond the bibliography

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

Open on alphaXiv

alphaXiv is searching for related work…

2011

Cited alongside, same era.

Z. Nussinov, G. Ortiz, and E. Cobanera, “Effective and exact holographies from symmetries and dualities,” Annals Phys

Original

2012

Cited alongside, same era.

T. Rudelius, N. Seiberg, and S.-H. Shao, “Fractons with Twisted Boundary Conditions and Their Symmetries,” Phys. Rev. B

Original

2012

Cited alongside, same era.

E. Cobanera, G. Ortiz, and Z. Nussinov, “Holographic symmetries and generalized order parameters for topological matter,” Phys. Rev. B

Original

2013

Cited alongside, same era.

S. Bravyi and J. Haah, “Quantum self-correction in the 3d cubic code model,” Phys. Rev. Lett

2013

Cited alongside, same era.

A. Kapustin and N. Seiberg, “Coupling a QFT to a TQFT and Duality,” JHEP

Original

2014

Cited alongside, same era.

D. Gaiotto, A. Kapustin, N. Seiberg, and B. Willett, “Generalized Global Symmetries,” JHEP

Original

2015

Cited alongside, same era.

P.-S. Hsin and N. Seiberg, “Level/rank Duality and Chern-Simons-Matter Theories,” JHEP

Original

2016

Cited alongside, same era.

Original

2021