  We present a comprehensive investigation of quantum oscillations (QOs) in the
strongly-correlated Falicov-Kimball model (FKM). The FKM is a particularly
suitable platform for probing the non-Fermi liquid state devoid of
quasiparticles, affording exact Monte Carlo simulation across all parameter
spaces. In the high-correlation regime, we report the presence of prominent QOs
in magnetoresistance and electron density at low temperatures within the phase
separation state. The frequency behavior of these oscillations uncovers a
transition in the Fermi surface as electron density diminishes, switching from
hole-like to electron-like. Both types of Fermi surfaces are found to conform
to the Onsager relation, establishing a connection between QOs frequency and
Fermi surface area. Upon exploring the temperature dependence of QOs amplitude,
we discern a strong alignment with the Lifshitz-Kosevich (LK) theory, provided
the effective mass is suitably renormalized. Notwithstanding, the substantial
enhancement of the overall effective mass results in a notable suppression of
the QOs amplitude within the examined temperature scope, a finding inconsistent
with Fermi liquid predictions. For the most part, the effective mass diminishes
as the temperature increases, but an unusual increase is observed at the
proximity of the second-order phase transition instigated by thermal effects.
As the transition ensues, the regular QOs disappear, replaced by irregular ones
in the non-Fermi liquid state under a high magnetic field. We also uncover
significant QOs in the insulating charge density wave state under weak
interactions ($0 < U < 1$), a phenomenon we elucidate through analytical
calculations. Our findings shed light on the critical role of quasiparticles in
the manifestation of QOs, enabling further understanding of their function in
this context.
