Weyl fermions on a finite lattice

TL;DR

This paper demonstrates that unpaired Weyl edge states with chiral, linear dispersion can be realized on a finite lattice using a Wilson fermion Hamiltonian in (2+1) dimensions, supporting chiral gauge theory regulation.

Contribution

It shows that Weyl-like boundary states appear on finite lattices, aligning with continuum boundary phenomena and aiding chiral gauge theory regulation.

Findings

Weyl edge states exhibit linear dispersion and definite chirality.

Boundary states circulate unidirectionally, confirming Weyl-like behavior.

Results are consistent with Nielsen-Ninomiya theorem.

Abstract

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.