Emergent Symmetry and Phase Transitions on the Domain Wall of $\mathbb{Z}_{2}$ Topological Orders
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866914262136389632 |
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| author | Song, Hong-Hao Peng, Chen Huang, Rui-Zhen Zhang, Long |
| author_facet | Song, Hong-Hao Peng, Chen Huang, Rui-Zhen Zhang, Long |
| contents | The one-dimensional (1D) domain wall of 2D $\mathbb{Z}_{2}$ topological orders is studied theoretically. The Ising domain wall model is shown to have an emergent SU(2)$_{1}$ conformal symmetry because of a hidden nonsymmorphic octahedral symmetry. While a weak magnetic field is an irrelevant perturbation to the bulk topological orders, it induces a domain wall transition from the Tomonaga-Luttinger liquid to a ferromagnetic order, which spontaneously breaks the anomalous $\mathbb{Z}_{2}$ symmetry and the time-reversal symmetry on the domain wall. Moreover, the gapless domain wall state also realizes a 1D topological quantum critical point between a $\mathbb{Z}_{2}^{T}$-symmetry-protected topological phase and a trivial phase, thus demonstrating the holographic construction of topological transitions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_12193 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Emergent Symmetry and Phase Transitions on the Domain Wall of $\mathbb{Z}_{2}$ Topological Orders Song, Hong-Hao Peng, Chen Huang, Rui-Zhen Zhang, Long Strongly Correlated Electrons Statistical Mechanics High Energy Physics - Theory The one-dimensional (1D) domain wall of 2D $\mathbb{Z}_{2}$ topological orders is studied theoretically. The Ising domain wall model is shown to have an emergent SU(2)$_{1}$ conformal symmetry because of a hidden nonsymmorphic octahedral symmetry. While a weak magnetic field is an irrelevant perturbation to the bulk topological orders, it induces a domain wall transition from the Tomonaga-Luttinger liquid to a ferromagnetic order, which spontaneously breaks the anomalous $\mathbb{Z}_{2}$ symmetry and the time-reversal symmetry on the domain wall. Moreover, the gapless domain wall state also realizes a 1D topological quantum critical point between a $\mathbb{Z}_{2}^{T}$-symmetry-protected topological phase and a trivial phase, thus demonstrating the holographic construction of topological transitions. |
| title | Emergent Symmetry and Phase Transitions on the Domain Wall of $\mathbb{Z}_{2}$ Topological Orders |
| topic | Strongly Correlated Electrons Statistical Mechanics High Energy Physics - Theory |
| url | https://arxiv.org/abs/2507.12193 |