Boundary modes in the Chamon model

Fontana, Weslei B.; Pereira, R. G. de A.

doi:10.21468/scipostphys.15.1.010

Cited by 5 publications

(3 citation statements)

References 66 publications

(112 reference statements)

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“…Similar observations have been made in a recent work about subsystem anomaly[56]. In the meantime, it was noticed that a single boundary anomaly may correspond to different bulk fracton models[57][58][59].…”

supporting

confidence: 87%

A Chern-Simons theory for dipole symmetry

Huang

2023

SciPost Phys.

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We present effective field theories for dipole symmetric topological matters that can be described by the Chern-Simons theory. Unlike most studies using higher-rank gauge theory, we develop a framework with both U(1)U(1) and dipole gauge fields. As a result, only the highest multipole symmetry can support the ’t Hooft anomaly. We show that with appropriate point group symmetries, the dipolar Chern-Simons theory can exist in any dimension and, moreover, the bulk-edge correspondence can depend on the boundary. As two applications, we draw an analogy between the dipole anomaly and the torsional anomaly and generalize particle-vortex duality to dipole phase transitions. All of the above are in the flat spacetime limit, but our framework is able to systematically couple dipole symmetry to curved spacetime. Based on that, we give a proposal about anomalous dipole hydrodynamics. Moreover, we show that the fracton-elasticity duality arises naturally from a non-abelian Chern-Simons theory in 3D.

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confidence: 87%

A Chern-Simons theory for dipole symmetry

Huang

2023

SciPost Phys.

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“…And each distinct sector of the Hilbert space of a lattice model can be the boundary of a (d + 1)dimensional model with topological orders, where the topological charge in the bulk determines the boundary sector 4. See also Ref [44]. that appeared soon after the first version of our arXiv preprint.…”

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confidence: 99%

Towards non-invertible anomalies from generalized Ising models

Liu,

2023

SciPost Phys.

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We present a general approach to the bulk-boundary correspondence of noninvertible topological phases, including both topological and fracton orders. This is achieved by a novel bulk construction protocol where solvable (d+1)(d+1)-dimensional bulk models with noninvertible topology are constructed from the so-called generalized Ising (GI) models in dd dimensions. The GI models can then terminate on the boundaries of the bulk models. The construction generates abundant examples, including not only prototype ones such as \mathbb{Z}_2ℤ2 toric code models in any dimensions no less than two, and the X-cube fracton model, but also more diverse ones such as the \mathbb{Z}_2x \mathbb{Z}_2ℤ2xℤ2 topological order, the 4d \mathbb{Z}_2ℤ2 topological order with pure-loop excitations, etc. The boundary of the solvable model is potentially anomalous and corresponds to precisely only sectors of the GI model that host certain total symmetry charges and/or satisfy certain boundary conditions. We derive a concrete condition for such bulk-boundary correspondence. The condition is violated only when the bulk model is either trivial or fracton ordered. A generalized notion of Kramers-Wannier duality plays an important role in the construction. Also, utilizing the duality, we find an example where a single anomalous theory can be realized on the boundaries of two distinct bulk fracton models, a phenomenon not expected in the case of topological orders. More generally, topological orders may also be generated starting with lattice models beyond the GI models, such as those with symmetry protected topological orders, through a variant bulk construction, which we provide in an appendix.

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“…Finally, subsystem SymTFT provides a bulk-boundary point of view to study subsystem symmetry. Recently, there are other efforts to study fracton models from bulk-boundary correspondence [82][83][84][85]. Subsystem SymTFT also provides hints to study fracton statistics [86,87].…”

Section: Jhep05(2024)225mentioning

confidence: 99%

Symmetry TFT for subsystem symmetry

Cao,

Jia

2024

J. High Energ. Phys.

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We generalize the idea of symmetry topological field theory (SymTFT) for subsystem symmetry. We propose the 2-foliated BF theory with level N in (3 + 1)d as subsystem SymTFT for subsystem ℤN symmetry in (2 + 1)d. Focusing on N = 2, we investigate various topological boundaries. The subsystem Kramers-Wannier and Jordan-Wigner dualities can be viewed as boundary transformations of the subsystem SymTFT and are included in a larger duality web from the subsystem SL(2, ℤ2) symmetry of the bulk foliated BF theory. Finally, we construct the condensation defects and twist defects of S-transformation in the subsystem SL(2, ℤ2), from which the fusion rule of subsystem non-invertible operators can be recovered.

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Boundary modes in the Chamon model

Cited by 5 publications

References 66 publications

A Chern-Simons theory for dipole symmetry

A Chern-Simons theory for dipole symmetry

Towards non-invertible anomalies from generalized Ising models

Symmetry TFT for subsystem symmetry

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