Non-Invertible Interfaces Between Symmetry-Enriched Critical Phases
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911344065773568 |
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| author | Prembabu, Saranesh Shao, Shu-Heng Verresen, Ruben |
| author_facet | Prembabu, Saranesh Shao, Shu-Heng Verresen, Ruben |
| contents | Gapless quantum phases can become distinct when internal symmetries are enforced, in analogy with gapped symmetry-protected topological (SPT) phases. However, this distinction does not always lead to protected edge modes, raising the question of how the bulk-boundary correspondence is generalized to gapless cases. We propose that the spatial interface between gapless phases -- rather than their boundaries -- provides a more robust fingerprint. We show that whenever two 1+1d conformal field theories (CFTs) differ in symmetry charge assignments of local operators or twisted sectors, any symmetry-preserving spatial interface between the theories must flow to a non-invertible defect. We illustrate this general result for different versions of the Ising CFT with $\mathbb{Z}_2 \times \mathbb{Z}_2^T$ symmetry, obtaining a complete classification of allowed conformal interfaces. When the Ising CFTs differ by nonlocal operator charges, the interface hosts 0+1d symmetry-breaking phases with finite-size splittings scaling as $1/L^3$, as well as continuous phase transitions between them. For general gapless phases differing by an SPT entangler, the interfaces between them can be mapped to conformal defects with a certain defect 't Hooft anomaly. This classification also gives implications for higher-dimensional examples, including symmetry-enriched variants of the 2+1d Ising CFT. Our results establish a physical indicator for symmetry-enriched criticality through symmetry-protected interfaces, giving a new handle on the interplay between topology and gapless phases. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_23706 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Non-Invertible Interfaces Between Symmetry-Enriched Critical Phases Prembabu, Saranesh Shao, Shu-Heng Verresen, Ruben Strongly Correlated Electrons Statistical Mechanics High Energy Physics - Theory Quantum Physics Gapless quantum phases can become distinct when internal symmetries are enforced, in analogy with gapped symmetry-protected topological (SPT) phases. However, this distinction does not always lead to protected edge modes, raising the question of how the bulk-boundary correspondence is generalized to gapless cases. We propose that the spatial interface between gapless phases -- rather than their boundaries -- provides a more robust fingerprint. We show that whenever two 1+1d conformal field theories (CFTs) differ in symmetry charge assignments of local operators or twisted sectors, any symmetry-preserving spatial interface between the theories must flow to a non-invertible defect. We illustrate this general result for different versions of the Ising CFT with $\mathbb{Z}_2 \times \mathbb{Z}_2^T$ symmetry, obtaining a complete classification of allowed conformal interfaces. When the Ising CFTs differ by nonlocal operator charges, the interface hosts 0+1d symmetry-breaking phases with finite-size splittings scaling as $1/L^3$, as well as continuous phase transitions between them. For general gapless phases differing by an SPT entangler, the interfaces between them can be mapped to conformal defects with a certain defect 't Hooft anomaly. This classification also gives implications for higher-dimensional examples, including symmetry-enriched variants of the 2+1d Ising CFT. Our results establish a physical indicator for symmetry-enriched criticality through symmetry-protected interfaces, giving a new handle on the interplay between topology and gapless phases. |
| title | Non-Invertible Interfaces Between Symmetry-Enriched Critical Phases |
| topic | Strongly Correlated Electrons Statistical Mechanics High Energy Physics - Theory Quantum Physics |
| url | https://arxiv.org/abs/2512.23706 |