Topological effect on order-disorder transitions in U(1) sigma models
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909651681935360 |
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| author | Shindou, Ryuichi Zhao, Pengwei |
| author_facet | Shindou, Ryuichi Zhao, Pengwei |
| contents | U(1) non-linear sigma model (NLSM) with a one-dimensional (1D) Berry phase is studied by a renormalization group theory. Order-disorder transition in U(1) NLSMs in $D \!\ (\ge 2)$-dimensional space ($d+1$-dimensional spacetime; $d\ge 1$) is instigated by the proliferation of vortex excitations, where the 1D Berry phase term confers finite phase factors upon those vortex excitations that have finite projection in a subspace complementary to a topological direction with the 1D Berry phase. A destructive interference effect caused by the phase factors may help to develop an intermediate quasi-disorder phase between ordered and disorder phases, which has a divergent order-parameter correlation length along the topological direction, and a finite correlation length along the other directions. In order to explore such a possibility in $D=3$, we develop a perturbative renormalization group theory of a 3D model of vortex loops, in which loop segments interact via a $1/r$ Coulomb interaction. We derive renormalization group (RG) equations among vortex-loop fugacity, Berry phase term, and the Coulomb potential. Approximate analyses of the RG equations show that near an order-disorder transition point, vortex loops are anomalously elongated along the topological direction. Utilizing a duality mapping to a lattice model of a type-II superconductor under a magnetic field, we also argue that a global phase diagram of the 3D U(1) sigma model with 1D Berry phase must have the quasi-disorder phase between ordered and disorder phases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_18969 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Topological effect on order-disorder transitions in U(1) sigma models Shindou, Ryuichi Zhao, Pengwei Strongly Correlated Electrons Disordered Systems and Neural Networks Quantum Gases Superconductivity U(1) non-linear sigma model (NLSM) with a one-dimensional (1D) Berry phase is studied by a renormalization group theory. Order-disorder transition in U(1) NLSMs in $D \!\ (\ge 2)$-dimensional space ($d+1$-dimensional spacetime; $d\ge 1$) is instigated by the proliferation of vortex excitations, where the 1D Berry phase term confers finite phase factors upon those vortex excitations that have finite projection in a subspace complementary to a topological direction with the 1D Berry phase. A destructive interference effect caused by the phase factors may help to develop an intermediate quasi-disorder phase between ordered and disorder phases, which has a divergent order-parameter correlation length along the topological direction, and a finite correlation length along the other directions. In order to explore such a possibility in $D=3$, we develop a perturbative renormalization group theory of a 3D model of vortex loops, in which loop segments interact via a $1/r$ Coulomb interaction. We derive renormalization group (RG) equations among vortex-loop fugacity, Berry phase term, and the Coulomb potential. Approximate analyses of the RG equations show that near an order-disorder transition point, vortex loops are anomalously elongated along the topological direction. Utilizing a duality mapping to a lattice model of a type-II superconductor under a magnetic field, we also argue that a global phase diagram of the 3D U(1) sigma model with 1D Berry phase must have the quasi-disorder phase between ordered and disorder phases. |
| title | Topological effect on order-disorder transitions in U(1) sigma models |
| topic | Strongly Correlated Electrons Disordered Systems and Neural Networks Quantum Gases Superconductivity |
| url | https://arxiv.org/abs/2503.18969 |