Astrophysical Quantum Matter Revisited: Flat-Band Topological States on a Zero-Flux Dipole Sphere
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915373388922880 |
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| author | Murugan, Jeff |
| author_facet | Murugan, Jeff |
| contents | We study strongly correlated fractional topological phases on a two-sphere threaded by a magnetic dipole field with globally vanishing flux. Solving the Dirac equation in this background produces spheroidal wavefunctions forming a highly degenerate manifold of normalizable zero modes, with degeneracy proportional to the total absolute flux. We introduce a non-Abelian spin gauge field near the equator to hybridize the north and south domain-confined modes, forming a global flat band. Projecting interactions into this band yields Laughlin-type correlated states. The entanglement spectrum shows a chiral tower consistent with a virtual edge, demonstrating bulk-edge correspondence in a closed geometry. This generalizes the zero-flux flat-band construction of \cite{Parhizkar:2024som} to curved backgrounds, with potential applications to synthetic and astrophysical systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_04363 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Astrophysical Quantum Matter Revisited: Flat-Band Topological States on a Zero-Flux Dipole Sphere Murugan, Jeff Strongly Correlated Electrons High Energy Astrophysical Phenomena High Energy Physics - Theory We study strongly correlated fractional topological phases on a two-sphere threaded by a magnetic dipole field with globally vanishing flux. Solving the Dirac equation in this background produces spheroidal wavefunctions forming a highly degenerate manifold of normalizable zero modes, with degeneracy proportional to the total absolute flux. We introduce a non-Abelian spin gauge field near the equator to hybridize the north and south domain-confined modes, forming a global flat band. Projecting interactions into this band yields Laughlin-type correlated states. The entanglement spectrum shows a chiral tower consistent with a virtual edge, demonstrating bulk-edge correspondence in a closed geometry. This generalizes the zero-flux flat-band construction of \cite{Parhizkar:2024som} to curved backgrounds, with potential applications to synthetic and astrophysical systems. |
| title | Astrophysical Quantum Matter Revisited: Flat-Band Topological States on a Zero-Flux Dipole Sphere |
| topic | Strongly Correlated Electrons High Energy Astrophysical Phenomena High Energy Physics - Theory |
| url | https://arxiv.org/abs/2507.04363 |