Winding number on 3D lattice
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916517644337152 |
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| author | Morikawa, Okuto Suzuki, Hiroshi |
| author_facet | Morikawa, Okuto Suzuki, Hiroshi |
| contents | We propose a simple numerical method which computes an approximate value of the winding number of a mapping from 3D torus~$T^3$ to the unitary group~$U(N)$, when $T^3$ is approximated by discrete lattice points. Our method consists of a ``tree-level improved'' discretization of the winding number and the gradient flow associated with an ``over-improved'' lattice action. By employing a one-parameter family of mappings from $T^3$ to $SU(2)$ with known winding numbers, we demonstrate that the method works quite well even for coarse lattices, reproducing integer winding numbers in a good accuracy. Our method can trivially be generalized to the case of higher-dimensional tori. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_03888 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Winding number on 3D lattice Morikawa, Okuto Suzuki, Hiroshi High Energy Physics - Lattice Mesoscale and Nanoscale Physics We propose a simple numerical method which computes an approximate value of the winding number of a mapping from 3D torus~$T^3$ to the unitary group~$U(N)$, when $T^3$ is approximated by discrete lattice points. Our method consists of a ``tree-level improved'' discretization of the winding number and the gradient flow associated with an ``over-improved'' lattice action. By employing a one-parameter family of mappings from $T^3$ to $SU(2)$ with known winding numbers, we demonstrate that the method works quite well even for coarse lattices, reproducing integer winding numbers in a good accuracy. Our method can trivially be generalized to the case of higher-dimensional tori. |
| title | Winding number on 3D lattice |
| topic | High Energy Physics - Lattice Mesoscale and Nanoscale Physics |
| url | https://arxiv.org/abs/2412.03888 |