Lieb-Schultz-Mattis-Type and Laughlin-Type Argument for the Quantum Hall Effect in Lattice Fermions with Spiral Boundary Conditions
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| Format: | Preprint |
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2025
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| _version_ | 1866912841442787328 |
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| author | Nakamura, Masaaki Yamanaka, Masanori |
| author_facet | Nakamura, Masaaki Yamanaka, Masanori |
| contents | We derive the condition for the occurrence of the integer quantum Hall effect in two-dimensional lattice systems with interactions, expressed as $ϕν-ρ\in\mathbb{Z}$, where $ϕ$, $ν$, and $ρ$ denote the magnetic flux, the Chern number, and the electron density, respectively. By employing spiral boundary conditions, which treat the system as an extended one-dimensional chain, this condition is obtained directly through a Lieb-Schultz-Mattis-type and Laughlin-type argument. This approach improves upon the preceding work based on conventional periodic boundary conditions, where the condition was derived indirectly with redundant system-size dependence. The key to this approach is that the spatial directions of the external force and the response can be systematically controlled by a factor of the system size. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_13594 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Lieb-Schultz-Mattis-Type and Laughlin-Type Argument for the Quantum Hall Effect in Lattice Fermions with Spiral Boundary Conditions Nakamura, Masaaki Yamanaka, Masanori Strongly Correlated Electrons Mesoscale and Nanoscale Physics We derive the condition for the occurrence of the integer quantum Hall effect in two-dimensional lattice systems with interactions, expressed as $ϕν-ρ\in\mathbb{Z}$, where $ϕ$, $ν$, and $ρ$ denote the magnetic flux, the Chern number, and the electron density, respectively. By employing spiral boundary conditions, which treat the system as an extended one-dimensional chain, this condition is obtained directly through a Lieb-Schultz-Mattis-type and Laughlin-type argument. This approach improves upon the preceding work based on conventional periodic boundary conditions, where the condition was derived indirectly with redundant system-size dependence. The key to this approach is that the spatial directions of the external force and the response can be systematically controlled by a factor of the system size. |
| title | Lieb-Schultz-Mattis-Type and Laughlin-Type Argument for the Quantum Hall Effect in Lattice Fermions with Spiral Boundary Conditions |
| topic | Strongly Correlated Electrons Mesoscale and Nanoscale Physics |
| url | https://arxiv.org/abs/2511.13594 |