(2+1)-dimensional compact Lifshitz theory, tensor gauge theory, and fractons

Gorantla, Pranay; Lam, Ho Tat; Seiberg, Nathan; Shao, Shu-Heng

doi:10.1103/physrevb.108.075106

Cited by 17 publications

(5 citation statements)

References 68 publications

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“…In this paper, we gave the first example of a subsystem non-invertible symmetry -the subsystem KW duality symmetry -in lattice models in (2 + 1)d, thereby filling in one missing To have a generic understanding of subsystem non-invertible symmetry, one can employ similar analysis to models with general abelian subsystem symmetry [83,175] or theories with global dipole symmetry [87,91]. Another interesting direction is to find the last missing corner in Tab.…”

Section: Discussion and Future Directionsmentioning

confidence: 99%

“…However, when the topologicalness is sacrificed as in the case of the subsystem symmetry, it is important to treat the symmetry operator and symmetry defect separately. The latter was highlighted recently [87,91] as a generator of the time-like symmetry.…”

Section: Symmetry Operators and Defectsmentioning

confidence: 98%

“…codimension invertibility topologicalness ordinary symmetry = 1 ✓ ✓ higher-form/group sym [1, ≥ 1 ✓ ✓ non-invertible/categorical sym = 1 ✗ ✓ higher categorical sym ≥ 1 ✗ ✓ subsystem sym [75][76][77][78][79][80][81][82][83][84][85][86][87][88][89][90][91] = 1 ✓ ✗ higher subsystem sym [141][142][143][144][145][146][147][148][149][150][151][152] ≥ 1 ✓ ✗ subsystem non-invertible sym = 1 ✗ ✗ higher subsystem non-invertible sym ≥ 1 ✗ ✗…”

Section: Symmetrymentioning

confidence: 99%

“…The remaining symmetries differ in one or multiple properties. For instance, higher-form symmetries relax the condition of codimension being one [1,; 1 non-invertible symmetries in (1 + 1)d relax the invertibility ; subsystem symmetries in (2 + 1)d relax the topologicalness or the mobility of the symmetry generators/defects 2 [75][76][77][78][79][80][81][82][83][84][85][86][87][88][89][90][91]. 3 Here and in Tab.…”

Section: Introduction 1subsystem Non-invertible Symmetrymentioning

confidence: 99%

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Subsystem non-invertible symmetry operators and defects

Cao,

Li,

Yamazaki

et al. 2023

SciPost Phys.

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We explore non-invertible symmetries in two-dimensional lattice models with subsystem \mathbb Z_2ℤ2 symmetry. We introduce a subsystem \mathbb Z_2ℤ2-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. Subsystem Kramers-Wannier duality defects are mobile in both spatial directions, unlike the defects of invertible subsystem symmetries. We finally comment on the anomaly of the subsystem Kramers-Wannier duality symmetry, and discuss its subtleties.

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Section: Discussion and Future Directionsmentioning

confidence: 99%

Section: Symmetry Operators and Defectsmentioning

confidence: 98%

Section: Symmetrymentioning

confidence: 99%

Section: Introduction 1subsystem Non-invertible Symmetrymentioning

confidence: 99%

See 2 more Smart Citations

Subsystem non-invertible symmetry operators and defects

Cao,

Li,

Yamazaki

et al. 2023

SciPost Phys.

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“…The model has also a winding subsystem symmetry associated with the conserved dipole [5,[18][19][20][21][22][23][24][25][26][27][28]. The winding symmetry can only be emergent in the XY-plaquette model, just like the winding symmetry of the XY-model in (1+1)d only emerges in a particular regime.…”

Section: Exotic Theoriesmentioning

confidence: 99%

Lattice quantum Villain Hamiltonians: compact scalars, U(1) gauge theories, fracton models and quantum Ising model dualities

Fazza

Sulejmanpašić

2023

J. High Energ. Phys.

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We construct Villain Hamiltonians for compact scalars and abelian gauge theories. The Villain integers are promoted to integral spectrum operators, whose canonical conjugates are naturally compact scalars. Further, depending on the theory, these conjugate operators can be interpreted as (higher-form) gauge fields. If a gauge symmetry is imposed on these dual gauge fields, a natural constraint on the Villain operator leads to the absence of defects (e.g. vortices, monopoles,…). These lattice models therefore have the same symmetry and anomaly structure as their corresponding continuum models. Moreover they can be formulated in a way that makes the well-know dualities look manifest, e.g. a compact scalar in 2d has a T-duality, in 3d is dual to a U(1) gauge theory, etc. We further discuss the gauged version of compact scalars on the lattice, its anomalies and solution, as well as a particular limit of the gauged XY model at strong coupling which reduces to the transverse-field Ising model. The construction for higher-form gauge theories is similar. We apply these ideas to the constructions of some models which are of interest to fracton physics, in particular the XY-plaquette model and the tensor gauge field model. The XY-plaquette model in 2+1d coupled to a tensor gauge fields at strong gauge coupling is also exactly described by a transverse field quantum J1 − J2 Ising model with J1 = 2J2, and discuss the phase structure of such models.

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Anomaly of subsystem symmetries in exotic and foliated BF theories

Shimamura

2024

J. High Energ. Phys.

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We study the mixed ’t Hooft anomaly of the subsystem symmetries in the exotic BF theory and the foliated BF theory in 2+1 dimensions, both of which are fractonic quantum field theories describing the equivalent physics. In the anomaly inflow mechanism, the ’t Hooft anomaly of the subsystem symmetries can be canceled by combining a subsystem symmetry-protected topological (SSPT) phase in one dimension higher. In this work, we construct the exotic and foliated BF theories with background gauge fields, and the exotic and foliated forms of the SSPT phases using the foliated-exotic duality. In the foliated form, we see that the non-topological defect that describes a fracton can be viewed as a symmetry-like operator. We also newly construct the foliated and exotic SSPT phases with different foliation structures via the foliated-exotic duality. We can show that the SSPT phases with different foliation structures cancel the same anomaly. This may provide a clue to the characterization of the ’t Hooft anomaly of subsystem symmetries.

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(2+1)-dimensional compact Lifshitz theory, tensor gauge theory, and fractons

Cited by 17 publications

References 68 publications

Subsystem non-invertible symmetry operators and defects

Subsystem non-invertible symmetry operators and defects

Lattice quantum Villain Hamiltonians: compact scalars, U(1) gauge theories, fracton models and quantum Ising model dualities

Anomaly of subsystem symmetries in exotic and foliated BF theories

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