  The kinetic energy of electrons in a magnetic field is quenched resulting in
a discrete set of highly degenerate Landau levels (LL) which gives rise to
fascinating phenomena like the de Haas-van Alphen effect (dHvAe) or the integer
and fractional quantum Hall effects. The latter is a result of interactions
partially lifting the degeneracy within a given LL while inter-LL interactions
are usually assumed to be unimportant. Here, we study the LL spectrum of the
Hatsugai-Kohmoto model, a Hubbard-like model which is exactly soluble on
account of infinite range interactions. For the doped Mott insulator phase in a
magnetic field we find that the degeneracy of LLs is preserved but inter-LL
interactions are important leading to a non-monotonous reconstruction of the
spectrum. As a result, strong LL repulsion leads to aperiodic quantum
oscillations of the dHvAe in contrast to Onsager's famous relation connecting
oscillation frequencies with the Fermi surface areas at zero field. In
addition, we find unconventional temperature dependencies of quantum
oscillations and interaction-induced effective mass renormalizations. We
discuss the general importance of inter-LL interactions for understanding doped
Mott insulators in magnetic fields.
