Equivalence of the staggered fermion Hamiltonan and the discrete Hodge-Dirac operator on square lattices
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914674377752576 |
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| author | Nakamura, Shu |
| author_facet | Nakamura, Shu |
| contents | We show that the free massless staggered fermion (or the KS-fermion) Hamiltonian is equivalent to a discrete Hodge-Dirac operator on the $d$-dimensional square lattice $h\mathbb{Z}^d$. In fact, they are identical operator valued matrices under suitable choices of their representations on $\ell^2(2h\mathbb{Z}^d)\otimes\mathbb{C}^{2^d}$. We employ the formulations of the staggered fermion by Nakamura (2024), and the discrete cohomology structure on the square lattices by Miranda-Parra (2023). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_07094 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Equivalence of the staggered fermion Hamiltonan and the discrete Hodge-Dirac operator on square lattices Nakamura, Shu Mathematical Physics 81Q35 We show that the free massless staggered fermion (or the KS-fermion) Hamiltonian is equivalent to a discrete Hodge-Dirac operator on the $d$-dimensional square lattice $h\mathbb{Z}^d$. In fact, they are identical operator valued matrices under suitable choices of their representations on $\ell^2(2h\mathbb{Z}^d)\otimes\mathbb{C}^{2^d}$. We employ the formulations of the staggered fermion by Nakamura (2024), and the discrete cohomology structure on the square lattices by Miranda-Parra (2023). |
| title | Equivalence of the staggered fermion Hamiltonan and the discrete Hodge-Dirac operator on square lattices |
| topic | Mathematical Physics 81Q35 |
| url | https://arxiv.org/abs/2402.07094 |