Low-Frequency Quantum Oscillations due to Strong Electron Correlations

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.