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Minimal-doubling and single-Weyl fermion Hamiltonians

Tatsuhiro Misumi*

  • *Contact author: misumi@phys.kindai.ac.jp
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Phys. Rev. D 113, 074521 – Published 28 April, 2026

DOI: https://doi.org/10.1103/jdy1-qw2s

Abstract

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 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 reexamine the non-on-site 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.

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Phys. Rev. D 113, 074521– Published 28 April, 2026
  • Received 6 January 2026
  • Accepted 9 April 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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