The Hubbard model in strong magnetic field: Low-frequency quantum oscillations due to strong electron correlations

The density of states of the two-dimensional fermionic Hubbard model in the perpendicular homogeneous magnetic field is calculated using the strong coupling diagram technique. The density of states at the Fermi level as a function of the inverse magnetic induction oscillates, and the frequency of these oscillations increases by an order of magnitude with the change of the deviation from half-filling from small to moderate values. This frequency variation is caused by the change of Landau subbands contributing to the density -- in the former case they are at the periphery of the Landau spectrum, while in the latter case the dominant contribution is provided by bands near its center. With changing induction these groups of bands behave differently. For small deviations from half-filling the calculated oscillation frequency is comparable to that observed in quantum oscillation experiments in yttrium cuprates.