Minimal-doubling and single-Weyl Hamiltonians
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866918471482212352 |
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| author | Misumi, Tatsuhiro |
| author_facet | Misumi, Tatsuhiro |
| contents | We develop a systematic Hamiltonian formulation of minimally doubled lattice fermions in (3+1) dimensions, derive their nodal structures (structures of zeros), and classify their symmetry patterns for both four-component Dirac and two-component Weyl constructions. Motivated by recent single-Weyl proposals based on Bogoliubov-de Gennes (BdG) representation, we argue that the corresponding single-Weyl Hamiltonians are obtained from the minimal-doubling Hamiltonians supplemented by an appropriate species-splitting mass term, and we re-examine the non-onsite symmetry protecting the physical Weyl node in terms of a Ginsparg-Wilson-type relation. We then construct a one-parameter family of deformations that preserves all the symmetries and demonstrate that, once the parameter exceeds a critical value, additional Weyl nodes emerge and the system exits the single-node regime. This indicates that in interacting theories radiative corrections can generate symmetry-allowed counterterms, so maintaining the desired single-Weyl phase generically requires "moderate" parameter tuning. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_22609 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Minimal-doubling and single-Weyl Hamiltonians Misumi, Tatsuhiro High Energy Physics - Lattice Strongly Correlated Electrons High Energy Physics - Theory We develop a systematic Hamiltonian formulation of minimally doubled lattice fermions in (3+1) dimensions, derive their nodal structures (structures of zeros), and classify their symmetry patterns for both four-component Dirac and two-component Weyl constructions. Motivated by recent single-Weyl proposals based on Bogoliubov-de Gennes (BdG) representation, we argue that the corresponding single-Weyl Hamiltonians are obtained from the minimal-doubling Hamiltonians supplemented by an appropriate species-splitting mass term, and we re-examine the non-onsite symmetry protecting the physical Weyl node in terms of a Ginsparg-Wilson-type relation. We then construct a one-parameter family of deformations that preserves all the symmetries and demonstrate that, once the parameter exceeds a critical value, additional Weyl nodes emerge and the system exits the single-node regime. This indicates that in interacting theories radiative corrections can generate symmetry-allowed counterterms, so maintaining the desired single-Weyl phase generically requires "moderate" parameter tuning. |
| title | Minimal-doubling and single-Weyl Hamiltonians |
| topic | High Energy Physics - Lattice Strongly Correlated Electrons High Energy Physics - Theory |
| url | https://arxiv.org/abs/2512.22609 |