Non-invertible duality and symmetry topological order of one-dimensional lattice models with spatially modulated symmetry
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909743946137600 |
|---|---|
| author | Seo, Donghae Cho, Gil Young Slager, Robert-Jan |
| author_facet | Seo, Donghae Cho, Gil Young Slager, Robert-Jan |
| contents | We investigate the interplay between self-duality and spatially modulated symmetry of generalized $N$-state clock models, which include the transverse-field Ising model and ordinary $N$-state clock models as special cases. The spatially modulated symmetry of the model becomes trivial when the model's parameters satisfy a specific number-theoretic relation. We find that the duality is non-invertible when the spatially modulated symmetry remains nontrivial, and show that this non-invertibility is resolved by introducing a generalized $\mathbb{Z}_N$ toric code, which manifests ultraviolet/infrared mixing, as the bulk topological order. In this framework, the boundary duality transformation corresponds to the boundary action of a bulk symmetry transformation, with the endpoint of the bulk symmetry defect realizing the boundary duality defect. Our results illuminate not only a holographic perspective on dualities but also a relationship between spatially modulated symmetry and ultraviolet/infrared mixing in one higher dimension. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_04182 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Non-invertible duality and symmetry topological order of one-dimensional lattice models with spatially modulated symmetry Seo, Donghae Cho, Gil Young Slager, Robert-Jan Strongly Correlated Electrons Statistical Mechanics High Energy Physics - Theory Mathematical Physics Quantum Physics We investigate the interplay between self-duality and spatially modulated symmetry of generalized $N$-state clock models, which include the transverse-field Ising model and ordinary $N$-state clock models as special cases. The spatially modulated symmetry of the model becomes trivial when the model's parameters satisfy a specific number-theoretic relation. We find that the duality is non-invertible when the spatially modulated symmetry remains nontrivial, and show that this non-invertibility is resolved by introducing a generalized $\mathbb{Z}_N$ toric code, which manifests ultraviolet/infrared mixing, as the bulk topological order. In this framework, the boundary duality transformation corresponds to the boundary action of a bulk symmetry transformation, with the endpoint of the bulk symmetry defect realizing the boundary duality defect. Our results illuminate not only a holographic perspective on dualities but also a relationship between spatially modulated symmetry and ultraviolet/infrared mixing in one higher dimension. |
| title | Non-invertible duality and symmetry topological order of one-dimensional lattice models with spatially modulated symmetry |
| topic | Strongly Correlated Electrons Statistical Mechanics High Energy Physics - Theory Mathematical Physics Quantum Physics |
| url | https://arxiv.org/abs/2411.04182 |