Algebra of Hyperbolic Band Theory under Magnetic Field
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866916139319164928 |
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| author | Ikeda, Kazuki Matsuki, Yoshiyuki Aoki, Shoto |
| author_facet | Ikeda, Kazuki Matsuki, Yoshiyuki Aoki, Shoto |
| contents | We explore algebras associated with the hyperbolic band theory under a magnetic field for the first time. We define the magnetic Fuchsian group associated with a higher genus Riemann surface. By imposing the magnetic boundary conditions for the hyperbolic Bloch states, we construct the hyperbolic magnetic Bloch states and investigate their energy spectrum. We give a connection between such magnetic Bloch states and automorphic forms. Our theory is a general extension of the conventional algebra associated with the band theory defined on a Euclidean lattice/space into that of the band theory on a general hyperbolic lattice/Riemann surface. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2107_10586 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Algebra of Hyperbolic Band Theory under Magnetic Field Ikeda, Kazuki Matsuki, Yoshiyuki Aoki, Shoto Mathematical Physics Mesoscale and Nanoscale Physics Algebraic Geometry Quantum Algebra Quantum Physics We explore algebras associated with the hyperbolic band theory under a magnetic field for the first time. We define the magnetic Fuchsian group associated with a higher genus Riemann surface. By imposing the magnetic boundary conditions for the hyperbolic Bloch states, we construct the hyperbolic magnetic Bloch states and investigate their energy spectrum. We give a connection between such magnetic Bloch states and automorphic forms. Our theory is a general extension of the conventional algebra associated with the band theory defined on a Euclidean lattice/space into that of the band theory on a general hyperbolic lattice/Riemann surface. |
| title | Algebra of Hyperbolic Band Theory under Magnetic Field |
| topic | Mathematical Physics Mesoscale and Nanoscale Physics Algebraic Geometry Quantum Algebra Quantum Physics |
| url | https://arxiv.org/abs/2107.10586 |