  We present first evidence for the Landau level structure of Dirac eigenmodes
in full QCD for nonzero background magnetic fields, based on first principles
lattice simulations using staggered quarks. Our approach involves the
identification of the lowest Landau level modes in two dimensions, where
topological arguments ensure a clear separation of these modes from
energetically higher states, and an expansion of the full four-dimensional
modes in the basis of these two-dimensional states. We evaluate various
fermionic observables including the quark condensate and the spin polarization
in this basis to find how much the lowest Landau level contributes to them. The
results allow for a deeper insight into the dynamics of quarks and gluons in
background magnetic fields and may be directly compared to low-energy models of
QCD employing the lowest Landau level approximation.
