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Weyl Fermions on a Finite Lattice

Dec 6, 2023
5 pages
Published in:
  • Phys.Rev.Lett. 132 (2024) 14, 141604
  • Published: Apr 2, 2024
e-Print:
DOI:
Report number:
  • INT-PUB-23-046
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Abstract: (APS)
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 D. B. Kaplan [preceding Letter, Chiral gauge theory at the boundary between topological phases, Phys. Rev. Lett. 132, 141603 (2024).]. 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 outlined in D. B. Kaplan, preceding Letter, for regulating chiral gauge theories.
Note:
  • 5 pages, 4 figures. This version coincides with the version accepted for publication in Phys. Rev. Lett. on Jan. 26, 2024. Major changes include performing computations on a disk-shaped lattice instead of square, with corresponding changes in the figures. Supplemental material of the publication version has been included here as an appendix. Scientific conclusions have not changed
  • fermion: Weyl
  • gauge field theory: chiral
  • fermion: Wilson
  • dispersion relation: linear
  • fermion: Dirac
  • boundary condition
  • lattice
  • Hamiltonian