Density of States of the Hubbard Model Supplemented with the Quantizing Magnetic Field

Using the strong coupling diagram technique, we calculate the zero-temperature density of states \(\rho\) of electrons on a square lattice immersed in a perpendicular uniform magnetic field. The electrons are described by Hubbard Hamiltonian. For moderate doping, Landau subbands are observed for small Hubbard repulsions U only. For larger U, the subbands are blurred. Instead, small peaks varying with the field induction B arise by opening the Mott gap in its vicinity. The related variation of \(\rho\) with 1/B may be connected with the low-frequency quantum oscillations in lightly doped cuprates. For all considered repulsions, \(\rho\) has gaps near transfer frequencies of the Hubbard atom, \(-\mu\) and \(U-\mu\), with \(\mu\) the chemical potential. In the heavily underdoped case \(\mu <0\), Landau subbands are grouped into the lower and upper Hubbard subbands for moderate and large repulsions. The intensity of the upper Hubbard subband decreases with approaching the Fermi level to the lower edge of the spectrum and finally vanishes.