Weyl fermions on a finite lattice
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866916159397298176 |
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| author | Kaplan, David B. Sen, Srimoyee |
| author_facet | Kaplan, David B. Sen, Srimoyee |
| contents | The phenomenon of unpaired Weyl fermions appearing on the sole 2n-dimensional boundary of a (2n+1)-dimensional manifold with massive Dirac fermions was recently analyzed in a companion paper by one of the authors. In this Letter we show that similar unpaired Weyl edge states can be seen on a finite lattice. In particular, we consider the discretized Hamiltonian for a Wilson fermion in (2+1) dimensions with a 1+1 dimensional boundary and continuous time. We demonstrate that the low lying boundary spectrum is indeed Weyl-like: it has a linear dispersion relation and definite chirality and circulates in only one direction around the boundary. We comment on how our results are consistent with Nielsen-Ninomiya theorem. This work removes one potential obstacle facing the program for regulating chiral gauge theories recently proposed by one of the authors. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2312_04012 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Weyl fermions on a finite lattice Kaplan, David B. Sen, Srimoyee High Energy Physics - Lattice Strongly Correlated Electrons High Energy Physics - Theory The phenomenon of unpaired Weyl fermions appearing on the sole 2n-dimensional boundary of a (2n+1)-dimensional manifold with massive Dirac fermions was recently analyzed in a companion paper by one of the authors. In this Letter we show that similar unpaired Weyl edge states can be seen on a finite lattice. In particular, we consider the discretized Hamiltonian for a Wilson fermion in (2+1) dimensions with a 1+1 dimensional boundary and continuous time. We demonstrate that the low lying boundary spectrum is indeed Weyl-like: it has a linear dispersion relation and definite chirality and circulates in only one direction around the boundary. We comment on how our results are consistent with Nielsen-Ninomiya theorem. This work removes one potential obstacle facing the program for regulating chiral gauge theories recently proposed by one of the authors. |
| title | Weyl fermions on a finite lattice |
| topic | High Energy Physics - Lattice Strongly Correlated Electrons High Energy Physics - Theory |
| url | https://arxiv.org/abs/2312.04012 |