Landau Levels in Lattice QCD

The spectrum of the two-dimensional continuum Dirac operator in the presence of a uniform background magnetic field consists of Landau levels, which are degenerate and separated by gaps. On the lattice the Landau levels are spread out by discretization artefacts, but a remnant of their structure is clearly visible (Hofstadter butterfly). If one switches on a non-Abelian interaction, the butterfly structure will be smeared out, but the lowest Landau level (LLL) will still be separated by a gap from the rest of the spectrum. In this talk we discuss how one can define the LLL in QCD and check how well certain physical quantities are approximated by taking into account only the LLL.