  The normal-state energy spectrum of the two-dimensional $t$-$J$ model in a
homogeneous perpendicular magnetic field is investigated. The density of states
at the Fermi level as a function of the inverse magnetic field $\frac{1}{B}$
reveals oscillations in the range of hole concentrations $0.08<x<0.18$. The
oscillations have both high- and low-frequency components. The former
components are connected with large Fermi surfaces, while the latter with van
Hove singularities in the Landau subbands, which traverse the Fermi level with
changing $B$. The singularities are related to bending the Landau subbands due
to strong electron correlations. Frequencies of these components are of the
same order of magnitude as quantum oscillation frequencies observed in
underdoped cuprates.
