Minimal-doubling and single-Weyl Hamiltonians

TL;DR

This paper systematically formulates minimally doubled lattice fermions in 3+1 dimensions, classifies their symmetries, and explores how single-Weyl phases can be maintained or disrupted through parameter tuning.

Contribution

It introduces a Hamiltonian framework for minimally doubled fermions, classifies their symmetry patterns, and analyzes the stability of single-Weyl phases under deformations.

Findings

Single-Weyl Hamiltonians derive from minimal-doubling Hamiltonians with a species-splitting mass.

A family of deformations can induce additional Weyl nodes beyond a critical parameter value.

Maintaining a single-Weyl phase requires moderate parameter tuning due to radiative corrections.

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.