  De Haas-van Alphen (dHvA) oscillations are oscillations in the magnetization
as a function of the inverse magnetic field. These oscillations are usually
considered to be a property of the Fermi surface and, hence, a metallic
property. Recently, however, such oscillations have been shown to arise, both
experimentally and theoretically, in certain insulators which have a narrow gap
and an inverted band structure. In this work, we develop a theory to study the
effect of many-body interaction on these unconventional oscillations. We
consider weak interaction, focusing on the effect of renormalization of the
quasiparticle spectrum on these oscillations. We find that interaction has an
unusual effect: unlike in metals, in a certain regime the amplitude of
oscillations may be enhanced substantially, both at zero and nonzero
temperatures, even when the interaction is perturbatively weak.
