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arXiv · 2605.27672

Spontaneous breaking of non-invertible symmetries and duality to beyond-Landau transitions

Xie Chen·Shang Liu·Da-chuan Lu·Nathanan Tantivasadakarn
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Abstract

Spontaneous symmetry breaking is a well-understood mechanism for generating distinct phases of matter. Recently, the notion of symmetry has been broadened to include operations without inverses, leading to the concept of non-invertible symmetries. How do symmetry-breaking phases associated with non-invertible symmetries differ from those arising from conventional invertible symmetries? We address this question using concrete lattice models of the gapped phases with non-invertible Rep($H_8$) symmetry as an example. We find that, despite the symmetry being non-invertible, the symmetry-breaking phases can still be characterized by the long-range correlation of local order parameters, which obey a more general algebraic structure than in the invertible setting. Furthermore, via generalized gauging, certain non-invertible symmetry-breaking transitions can be mapped to deconfined quantum critical points of invertible symmetries, and vice versa. We establish precise conditions under which this duality holds and illustrate them with several families of examples, providing a systematic route to studying beyond-Landau phase transitions.

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Xie Chen, Shang Liu, Da-chuan Lu, Nathanan Tantivasadakarn. 2026-05-26. Spontaneous breaking of non-invertible symmetries and duality to beyond-Landau transitions. https://arxiv.org/abs/2605.27672

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