Yang-Mills gauge theories from fermionic lattice models
arXiv:0807.0826 · doi:10.1016/j.physleta.2009.05.029
Abstract
A doublet of three-dimensional Dirac fermions can effectively describe the low energy spectrum of a fermionic cubic lattice. We employ this fermion doubling to encode a non-Abelian SU(2) charge in the fundamental representation. We explicitly demonstrate that suitable distortion of the tunnelling couplings can introduce a scalar and a Yang-Mills field in the effective low energy description, both coupled to the Dirac fermions. As an application we simulate Yang-Mills monopoles that give rise to localized zero-modes and fermion fractionalization. The generation of the non-Abelian field in the two-dimensional case is also presented.
10 pages, 1 figure, to appear in Phys. Lett. A
References in corpus (10)
- Creation of effective magnetic fields in optical lattices: The Hofstadter butterfly for cold neutral atoms
- Strongly correlated 2D quantum phases with cold polar molecules: controlling the shape of the interaction potential
- Electron fractionalization in two-dimensional graphenelike structures
- Cold atoms in non-Abelian gauge potentials: From the Hofstadter "moth" to lattice gauge theory
- Chiral Gauge Theory for Graphene
- Origin of Light
- Irrational vs. rational charge and statistics in two-dimensional quantum systems
- Fractionalization in a square-lattice model with time-reversal symmetry
- The Low-Lying Dirac Spectrum of Staggered Quarks
- Graphene with geometrically induced vorticity
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