Dualization of ingappabilities through Hilbert-space extensions
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866912016176775168 |
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| author | Yao, Yuan |
| author_facet | Yao, Yuan |
| contents | Typical dualities in arbitrary dimensions are understood through a Hilbert-space extension method. By these results, we rigorously dualize the quantum ingappabilities to discrete height model in one dimension which is inaccessible by earlier work such as flux-insertion arguments. It turns out that the ingappabilities of quantum discrete height model is protected by an exotic "modulating" translation symmetry, which is a combination of modulating internal symmetry transformation and the conventional lattice translation. It can be also generalize to higher-form gauge fields in arbitrary dimensions, e.g., $\mathbb{Z}$-gauge theory in two dimensions with $\mathbb{Z}$ one-form symmetry and a modulating translation symmetry. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_01972 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Dualization of ingappabilities through Hilbert-space extensions Yao, Yuan Strongly Correlated Electrons Statistical Mechanics High Energy Physics - Lattice High Energy Physics - Theory Mathematical Physics Typical dualities in arbitrary dimensions are understood through a Hilbert-space extension method. By these results, we rigorously dualize the quantum ingappabilities to discrete height model in one dimension which is inaccessible by earlier work such as flux-insertion arguments. It turns out that the ingappabilities of quantum discrete height model is protected by an exotic "modulating" translation symmetry, which is a combination of modulating internal symmetry transformation and the conventional lattice translation. It can be also generalize to higher-form gauge fields in arbitrary dimensions, e.g., $\mathbb{Z}$-gauge theory in two dimensions with $\mathbb{Z}$ one-form symmetry and a modulating translation symmetry. |
| title | Dualization of ingappabilities through Hilbert-space extensions |
| topic | Strongly Correlated Electrons Statistical Mechanics High Energy Physics - Lattice High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2409.01972 |