Topological Aspects of Fermions on a Honeycomb Lattice

Details Topological Aspects of Fermions on a Honeycomb Lattice Topological Aspects of Fermions on a Honeycomb Lattice

2009-04-08

arxiv.org/abs/0904.1310v2

JHEP 0906:060,2009

Physics

High Energy Physics

High Energy Physics - Lattice

LaTeX, 20 pages, 12 eps figures. Added minor modifications and references. Published on JHEP

Scientific paper

10.1088/1126-6708/2009/06/060

We formulate a model of relativistic fermions moving in two Euclidean dimensions based on a tight-binding model of graphene. The eigenvalue spectrum of the resulting Dirac operator is solved numerically in smooth U(1) gauge field backgrounds carrying an integer-valued topological charge Q, and it is demonstrated that the resulting number of zero-eigenvalue modes is in accord with the Atiyah-Singer index theorem applied to two continuum flavors. A bilinear but gauge non-invariant chirality operator appropriate for distinguishing the topological zero modes is identified. When this operator is used to calculate Q, it is found that the maximum topological charge capable of being measured in this fashion scales with the perimeter of the lattice. Some concluding remarks compare these results to what is known for staggered lattice fermions.

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