Massive Higher-Spin Fields in the Fractional Quantum Hall Effect
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866917883737538560 |
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| author | Bergshoeff, Eric Campoleoni, Andrea Palumbo, Giandomenico Salgado-Rebolledo, Patricio |
| author_facet | Bergshoeff, Eric Campoleoni, Andrea Palumbo, Giandomenico Salgado-Rebolledo, Patricio |
| contents | Incompressibility plays a key role in the geometric description of fractional quantum Hall fluids. It is naturally related to quantum area-preserving diffeomorphisms and the underlying Girvin-MacDonald-Plazman algebra, which gives rise to an emergent non-relativistic massive spin-2 mode propagating in the bulk. The corresponding metric tensor can be identified with a nematic order parameter for the bulk states. In the linearised regime with a flat background, it has been shown that this mode can be described by a spin-2 Schroedinger action. However, quantum area-preserving diffeomorphisms also suggest the existence of higher-spin modes that cannot be described through nematic fractional quantum Hall states. Here, we consider p-atic Hall phases, in which the corresponding p-atic order parameters are related to higher-rank symmetric tensors. We then show that in this framework, non-relativistic massive chiral higher-spin fields naturally emerge and that their dynamics is described by higher-spin Schroedinger actions. We finally show that these effective actions can be derived from relativistic massive higher-spin theories in 2+1 dimensions after taking a non-relativistic limit. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_16013 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Massive Higher-Spin Fields in the Fractional Quantum Hall Effect Bergshoeff, Eric Campoleoni, Andrea Palumbo, Giandomenico Salgado-Rebolledo, Patricio Strongly Correlated Electrons Mesoscale and Nanoscale Physics High Energy Physics - Theory Incompressibility plays a key role in the geometric description of fractional quantum Hall fluids. It is naturally related to quantum area-preserving diffeomorphisms and the underlying Girvin-MacDonald-Plazman algebra, which gives rise to an emergent non-relativistic massive spin-2 mode propagating in the bulk. The corresponding metric tensor can be identified with a nematic order parameter for the bulk states. In the linearised regime with a flat background, it has been shown that this mode can be described by a spin-2 Schroedinger action. However, quantum area-preserving diffeomorphisms also suggest the existence of higher-spin modes that cannot be described through nematic fractional quantum Hall states. Here, we consider p-atic Hall phases, in which the corresponding p-atic order parameters are related to higher-rank symmetric tensors. We then show that in this framework, non-relativistic massive chiral higher-spin fields naturally emerge and that their dynamics is described by higher-spin Schroedinger actions. We finally show that these effective actions can be derived from relativistic massive higher-spin theories in 2+1 dimensions after taking a non-relativistic limit. |
| title | Massive Higher-Spin Fields in the Fractional Quantum Hall Effect |
| topic | Strongly Correlated Electrons Mesoscale and Nanoscale Physics High Energy Physics - Theory |
| url | https://arxiv.org/abs/2404.16013 |