Minimal-doubling and single-Weyl Hamiltonians

TL;DR

This work develops a Hamiltonian framework for minimally doubled lattice fermions in $3+1$ dimensions, deriving their nodal structures and symmetry properties for Dirac and Weyl realizations. It systematically connects these constructions to BdG-based single-Weyl proposals and frames the chiral structure in a Hamiltonian Ginsparg-Wilson–like form, including a non-onsite chiral generator. A symmetry-preserving one-parameter deformation is shown to move and potentially create extra Weyl nodes beyond a critical threshold, implying that radiative corrections in interacting theories can generate counterterms and necessitate tuning to maintain a single Weyl node. The results highlight design principles for robust single-Weyl lattice models and motivate numerical phase-diagram studies to understand the stability of the single-node regime under gauge interactions and radiative effects.

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 (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.