Invertible Symmetry and Spontaneous Duality Breaking in the Transverse-Field Ising Model

• URL: http://arxiv.org/abs/2605.13363v1
• Date: Wed, 13 May 2026 11:24:09 GMT
• Title: Invertible Symmetry and Spontaneous Duality Breaking in the Transverse-Field Ising Model
• Abstract summary: The self-duality of the transverse-field Ising model is an archetype for dualities that, alongside symmetry and topology, are used as an organizing principle throughout modern physics.<n>Here, we show that by adjusting the model to accommodate open rather than periodic boundary conditions, it allows for an exact duality.<n>In the model with exact duality, the symmetry at the quantum critical point is also exact, and hence invertible.<n>Finally, the exactness of the duality implies that the spontaneous breakdown of a global symmetry in terms of the original model can equivalently be described as spontaneously breaking a local symmetry in
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The self-duality of the transverse-field Ising model is an archetype for dualities that, alongside symmetry and topology, are used as an organizing principle throughout modern physics. This duality, however, is not exact. The original and dual models have different symmetries and numbers of ground states, and the duality is implemented by a non-invertible operator giving rise to a non-invertible symmetry at the quantum critical point. Here, we show that by adjusting the model to accommodate open rather than periodic boundary conditions, it allows for an exact duality implemented by a unique invertible operator. In the model with exact duality, the symmetry at the quantum critical point is also exact, and hence invertible. Moreover, we find that the exact duality necessitates the presence of an anomalous edge degree of freedom, thus realizing a duality rather than topology based bulk-boundary correspondence. Finally, the exactness of the duality implies that the spontaneous breakdown of a global symmetry in terms of the original model can equivalently be described as spontaneously breaking a local symmetry in the dual system. We show that this seeming contradiction of Elitzur's theorem can be explained by the original and dual models obtaining different sensitivities to spatially local perturbations in any physical implementation of the Hamiltonian. Although the dual partners are mathematically equivalent, their physical implementations therefore are not. In analogy to the spontaneous breakdown of symmetries, we term this emergent distinction due to arbitrarily small environmental influences spontaneous duality breaking.

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