  The availability of large magnetic fields at international facilities and of
simulated magnetic fields that can reach the flux-quantum-per-unit-area level
in cold atoms, calls for systematic studies of orbital effects of the magnetic
field on the self-energy of interacting systems. Here we demonstrate
theoretically that orbital effects of magnetic fields can be treated within
single-site dynamical mean-field theory with a translationally invariant
quantum impurity problem. As an example, we study the one-band Hubbard model on
the square lattice using iterated perturbation theory as an impurity solver. We
recover the expected quantum oscillations in the scattering rate and we show
that the magnetic fields allow the interaction-induced effective mass to be
measured through the single-particle density of states accessible in tunneling
experiments. The orbital effect of magnetic fields on scattering becomes
particularly important in the Hofstadter butterfly regime.
