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| Format: | Preprint |
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2024
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| Accès en ligne: | https://arxiv.org/abs/2403.16017 |
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| _version_ | 1866911818706845696 |
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| author | Yan, Han Li, Linhao |
| author_facet | Yan, Han Li, Linhao |
| contents | We present the Bilinear Phase Map (BPM), a concept that extends the Kramers-Wannier (KW) transformation to investigate unconventional gapped phases, their dualities, and phase transitions. Defined by a matrix of $\mathbb{Z}_2$ elements, the BPM not only encapsulates the essence of KW duality but also enables exploration of a broader spectrum of generalized quantum phases and dualities. By analyzing the BPM's linear algebraic properties, we elucidate the loss of unitarity in duality transformations and derive general non-invertible fusion rules. Applying this framework to (1+1)D systems yields the discovery of new dualities, shedding light on the interplay between various Symmetry Protected Topological (SPT) and Spontaneous Symmetry Breaking (SSB) phases. Additionally, we construct a duality web that interconnects these phases and their transitions, offering valuable insights into relations between different quantum phases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_16017 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Generalized Kramers-Wanier Duality from Bilinear Phase Map Yan, Han Li, Linhao Strongly Correlated Electrons Statistical Mechanics Mathematical Physics We present the Bilinear Phase Map (BPM), a concept that extends the Kramers-Wannier (KW) transformation to investigate unconventional gapped phases, their dualities, and phase transitions. Defined by a matrix of $\mathbb{Z}_2$ elements, the BPM not only encapsulates the essence of KW duality but also enables exploration of a broader spectrum of generalized quantum phases and dualities. By analyzing the BPM's linear algebraic properties, we elucidate the loss of unitarity in duality transformations and derive general non-invertible fusion rules. Applying this framework to (1+1)D systems yields the discovery of new dualities, shedding light on the interplay between various Symmetry Protected Topological (SPT) and Spontaneous Symmetry Breaking (SSB) phases. Additionally, we construct a duality web that interconnects these phases and their transitions, offering valuable insights into relations between different quantum phases. |
| title | Generalized Kramers-Wanier Duality from Bilinear Phase Map |
| topic | Strongly Correlated Electrons Statistical Mechanics Mathematical Physics |
| url | https://arxiv.org/abs/2403.16017 |