Hofstadter problem in higher dimensions
arXiv:1210.6355 · doi:10.1093/ptep/ptu144
Abstract
We investigate some generalizations of the Hofstadter problem to higher dimensions with Abelian and non-Abelian gauge field configurations. We numerically show the hierarchical structure in the energy spectra with several lattice models. It is also pointed out the equivalence betwee the π-flux state and the staggered formalism of Dirac fermion.
1+15 pages, 2 figures; minor corrections, references added
References in corpus (17)
- Topological Field Theory of Time-Reversal Invariant Insulators
- Realization of the Hofstadter Hamiltonian with ultracold atoms in optical lattices
- Realizing the Harper Hamiltonian with Laser-Assisted Tunneling in Optical Lattices
- Three-Dimensional Topological Insulators
- Non-Abelian optical lattices: Anomalous quantum Hall effect and Dirac Fermions
- Ultracold atomic gas in non-Abelian "magnetic" fields: the quantum Hall effect supremacy
- Ultracold atomic gases in non-Abelian gauge potentials: The case of constant Wilson loop
- Time-Reversal-Invariant Hofstadter-Hubbard Model with Ultracold Fermions
- Quantum Hall effect and the topological number in graphene
- Hofstadter butterflies of bilayer graphene
- Hofstadter butterflies of carbon nanotubes: Pseudofractality of the magnetoelectronic spectrum
- Single flavor staggered fermions
- Pairs of chiral quarks on the lattice from staggered fermions
- Quantum Hall-like effect for cold atoms in non-Abelian gauge potentials
- Emergent spin
- Spatial patterns in optical lattices submitted to gauge potentials
- Hofstadter Problem on the Honeycomb and Triangular Lattices: Bethe Ansatz Solution