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Indirect Fabrication of Lattice Metals with Thin Sections Using Centrifugal Casting
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Weyl Fermions on a Finite Lattice.

David B Kaplan1, Srimoyee Sen2

  • 1Institute for Nuclear Theory, Box 351550, Seattle, Washington 98195-1550, USA.

Physical Review Letters
|April 19, 2024
PubMed
Summary

Unpaired Weyl fermions, crucial for chiral gauge theories, are shown to exist on finite lattices. This finding supports theoretical models by demonstrating Weyl edge states in a (2+1)-dimensional discretized system.

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.

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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.