Self-dual Higgs transitions: Toric code and beyond
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866908795594080256 |
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| author | Ji, Wenjie Lanzetta, Ryan A. Zhou, Zheng Wang, Chong |
| author_facet | Ji, Wenjie Lanzetta, Ryan A. Zhou, Zheng Wang, Chong |
| contents | The toric code, when deformed in a way that preserves the self-duality $\mathbb{Z}_2$ symmetry exchanging the electric and magnetic excitations, admits a transition to a topologically trivial state that spontaneously breaks the $\mathbb{Z}_2$ symmetry. Numerically, this transition was found to be continuous, which makes it particularly enigmatic given the longstanding absence of a continuum field-theoretic description. In this work we propose such a continuum field theory for the transition dubbed the $SO(4)_{2,-2}$ Chern-Simons-Higgs (CSH) theory. We show that our field theory provides a natural "mean-field" understanding of the phase diagram. Moreover, it can be generalized to an entire series of theories, namely the $SO(4)_{k,-k}$ CSH theories, labeled by an integer $k$. For each $k>2$, the theory describes an analogous transition involving different non-Abelian topological orders, such as the double Fibonacci order ($k=3$) and the $S_3$ quantum double ($k=4$). For $k=1$, we conjecture that the corresponding CSH transition is in fact infrared-dual to the $3d$ Ising transition, in close analogy with the particle-vortex duality of a complex scalar. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_20945 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Self-dual Higgs transitions: Toric code and beyond Ji, Wenjie Lanzetta, Ryan A. Zhou, Zheng Wang, Chong Strongly Correlated Electrons Statistical Mechanics High Energy Physics - Theory The toric code, when deformed in a way that preserves the self-duality $\mathbb{Z}_2$ symmetry exchanging the electric and magnetic excitations, admits a transition to a topologically trivial state that spontaneously breaks the $\mathbb{Z}_2$ symmetry. Numerically, this transition was found to be continuous, which makes it particularly enigmatic given the longstanding absence of a continuum field-theoretic description. In this work we propose such a continuum field theory for the transition dubbed the $SO(4)_{2,-2}$ Chern-Simons-Higgs (CSH) theory. We show that our field theory provides a natural "mean-field" understanding of the phase diagram. Moreover, it can be generalized to an entire series of theories, namely the $SO(4)_{k,-k}$ CSH theories, labeled by an integer $k$. For each $k>2$, the theory describes an analogous transition involving different non-Abelian topological orders, such as the double Fibonacci order ($k=3$) and the $S_3$ quantum double ($k=4$). For $k=1$, we conjecture that the corresponding CSH transition is in fact infrared-dual to the $3d$ Ising transition, in close analogy with the particle-vortex duality of a complex scalar. |
| title | Self-dual Higgs transitions: Toric code and beyond |
| topic | Strongly Correlated Electrons Statistical Mechanics High Energy Physics - Theory |
| url | https://arxiv.org/abs/2601.20945 |