Strongly correlated electron system in the magnetic field

The energy spectrum of the two-dimensional t-J model in a 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 $0.08<x<0.18$. In the used approximation zero-field Fermi surfaces are large for these $x$, and oscillation frequencies conform with such Fermi surfaces. However, the amplitude of these oscillations is modulated with a frequency which is smaller by an order of magnitude. The appearance of this modulation is related to van Hove singularities in the Landau subbands, which traverse the Fermi level with changing $B$. The singularities are connected with bending the Landau subbands due to strong electron correlations. The frequency of the modulation is of the same order of magnitude as the quantum oscillation frequency observed in underdoped cuprates.