Weyl Fermions on a Finite Lattice

Area of Science:

• Condensed Matter Physics
• High Energy Physics
• Theoretical Physics

Background:

• Unpaired Weyl fermions were recently analyzed on the boundary of higher-dimensional manifolds.
• Chiral gauge theories require specific boundary states for regularization.

Purpose of the Study:

• To demonstrate the existence of unpaired Weyl edge states on a finite lattice.
• To investigate the properties of these states in a (2+1)-dimensional discretized system.
• To address challenges in regulating chiral gauge theories.

Main Methods:

• Discretized Hamiltonian for Wilson fermion in (2+1) dimensions.
• Analysis of the 1+1 dimensional boundary spectrum.
• Continuous time evolution.

Main Results:

• Low-lying boundary spectrum exhibits Weyl-like characteristics.
• Observed linear dispersion relation and definite chirality.
• Demonstrated unidirectional circulation of states around the boundary.

Conclusions:

• The results are consistent with the Nielsen-Ninomiya theorem.
• This work validates the existence of Weyl edge states on finite lattices.
• It removes a key obstacle for regulating chiral gauge theories as proposed by D.B. Kaplan.