Non-Invertible Duality Transformation Between SPT and SSB Phases
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2023
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866913275140112384 |
|---|---|
| author | Li, Linhao Oshikawa, Masaki Zheng, Yunqin |
| author_facet | Li, Linhao Oshikawa, Masaki Zheng, Yunqin |
| contents | In 1992, Kennedy and Tasaki constructed a non-local unitary transformation that maps between a $\mathbb{Z}_2\times \mathbb{Z}_2$ spontaneously symmetry breaking phase and the Haldane gap phase, which is a prototypical Symmetry-Protected Topological phase in modern framework, on an open spin chain. In this work, we propose a way to define it on a closed chain, by sacrificing unitarity. The operator realizing such a non-unitary transformation satisfies non-invertible fusion rule, and implements a generalized gauging of the $\mathbb{Z}_2\times \mathbb{Z}_2$ global symmetry. These findings connect the Kennedy-Tasaki transformation to numerous other concepts developed for SPT phases, and opens a way to construct SPT phases systematically using the duality mapping. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_07899 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Non-Invertible Duality Transformation Between SPT and SSB Phases Li, Linhao Oshikawa, Masaki Zheng, Yunqin Strongly Correlated Electrons High Energy Physics - Theory In 1992, Kennedy and Tasaki constructed a non-local unitary transformation that maps between a $\mathbb{Z}_2\times \mathbb{Z}_2$ spontaneously symmetry breaking phase and the Haldane gap phase, which is a prototypical Symmetry-Protected Topological phase in modern framework, on an open spin chain. In this work, we propose a way to define it on a closed chain, by sacrificing unitarity. The operator realizing such a non-unitary transformation satisfies non-invertible fusion rule, and implements a generalized gauging of the $\mathbb{Z}_2\times \mathbb{Z}_2$ global symmetry. These findings connect the Kennedy-Tasaki transformation to numerous other concepts developed for SPT phases, and opens a way to construct SPT phases systematically using the duality mapping. |
| title | Non-Invertible Duality Transformation Between SPT and SSB Phases |
| topic | Strongly Correlated Electrons High Energy Physics - Theory |
| url | https://arxiv.org/abs/2301.07899 |