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| Main Authors: | , |
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| Format: | Preprint |
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2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2507.19401 |
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| _version_ | 1866916866759327744 |
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| author | How, Pye Ton Yip, Sungkit |
| author_facet | How, Pye Ton Yip, Sungkit |
| contents | We formulate a duality transformation for a bilayer XY model where the layers are coupled by second order Josephson effect, which favors inter-layer phase difference of either $0$ or $π$. The model may represent a bilayer superconductor or a spin-1 ferromagnetic Bose gas in the easy-plane limit. The second order Josephson term is mapped to a U(1) gauge field, known to be trivially confining in two dimensions, and we argue that a Coulomb-gas analysis is not applicable to the dual theory. Instead, we appeal to the vast knowledge of gauge theory and infer that the only phase transition out of low-temperature ordered phase is an Ising transition driven by condensation of $\mathbb{Z}_2$ domain wall loops. The domain wall loops can be seen as a surviving vestige of single-layer vortex-anti-vortex pair, heavily deformed by the second order Josephson coupling. A theoretical or computational method that concentrates on point defects would most likely miss out on these excitations and reach erroneous results. Our dual theory offers a clear, intuitive picture of how the second order Josephson coupling induces confinement of vortices and drastically changes the physics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_19401 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The gauge theory dual of the bilayer XY model with second order Josephson coupling How, Pye Ton Yip, Sungkit Superconductivity We formulate a duality transformation for a bilayer XY model where the layers are coupled by second order Josephson effect, which favors inter-layer phase difference of either $0$ or $π$. The model may represent a bilayer superconductor or a spin-1 ferromagnetic Bose gas in the easy-plane limit. The second order Josephson term is mapped to a U(1) gauge field, known to be trivially confining in two dimensions, and we argue that a Coulomb-gas analysis is not applicable to the dual theory. Instead, we appeal to the vast knowledge of gauge theory and infer that the only phase transition out of low-temperature ordered phase is an Ising transition driven by condensation of $\mathbb{Z}_2$ domain wall loops. The domain wall loops can be seen as a surviving vestige of single-layer vortex-anti-vortex pair, heavily deformed by the second order Josephson coupling. A theoretical or computational method that concentrates on point defects would most likely miss out on these excitations and reach erroneous results. Our dual theory offers a clear, intuitive picture of how the second order Josephson coupling induces confinement of vortices and drastically changes the physics. |
| title | The gauge theory dual of the bilayer XY model with second order Josephson coupling |
| topic | Superconductivity |
| url | https://arxiv.org/abs/2507.19401 |