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Generating Lattice Non-invertible Symmetries
by Weiguang Cao, Linhao Li, Masahito Yamazaki
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Submission summary
| Authors (as registered SciPost users): | Weiguang Cao |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202408_00009v1 (pdf) |
| Date accepted: | 2024-09-09 |
| Date submitted: | 2024-08-10 15:06 |
| Submitted by: | Cao, Weiguang |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
Lattice non-invertible symmetries have rich fusion structures and play important roles in understanding various exotic topological phases. In this paper, we explore methods to generate new lattice non-invertible transformations/symmetries from a given non-invertible seed transformation/symmetry. The new lattice non-invertible symmetry is constructed by composing the seed transformations on different sites or sandwiching a unitary transformation between the transformations on the same sites. In addition to known non-invertible symmetries with fusion algebras of Tambara-Yamagami $\mathbb Z_N\times\mathbb Z_N$ type, we obtain a new non-invertible symmetry in models with $\mathbb Z_N$ dipole symmetries. We name the latter the dipole Kramers-Wannier symmetry because it arises from gauging the dipole symmetry. We further study the dipole Kramers-Wannier symmetry in depth, including its topological defect, its anomaly and its associated generalized Kennedy-Tasaki transformation.
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List of changes
We fixed the issues as the first referee suggested.
To respond the second referee's comment, we added a comment around Eq. (2.29) in page 10 to show that the the other $Z_N$ symmetry generated by $\prod_{i=1}^L Z_i$ becomes the dipole symmetry in the dipole ising model. We add the details about promoting the global symmetry to gauge symmetry below Eq.(3.2). Now the Gauss law condition can be seen directly from the gauge transformation (new Eq.(3.7) ). About the second point, we didn’t ignore the Gauss law constraints but impose the constraints to reduce the enlarged Hilbert space of the gauge theory to a new Hilbert space with dimension 2^L. To highlight this point, we added a sentence “Afte imposing the Gauss law constraints, the enlarged Hilbert space $\tilde{\mathcal{H}}$ is projected down to a new Hilbert space with dimension $2^{L}$, which is isomorphic to the original Hilbert space $\mathcal{H}$.”
Published as SciPost Phys. 17, 104 (2024)
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All the previous comments have been addressed in the new version of the manuscript. It is recommended that the paper is published in its current form.
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