Harper’s equation for two-dimensional systems of antiferromagnetically correlated electrons

Considering interacting (antiferromagnetically correlated) electrons, we derive a generalized Harper’s equation in a mean-field approximation for a square lattice of infinite size. In the present study with the aid of a gap equation we explain the cause of the oscillatory behavior in staggered magnetization with the variation of an applied magnetic field for two-dimensional systems of antiferromagnetically correlated electrons. Exact diagonalization calculations on small clusters show additional evidence for the oscillatory behavior of staggered magnetization. We find that for systems of weakly correlated electrons both mean-field and exact diagonalization calculations yield an identical behavior in the propensity of diminishing staggered magnetization for even-denominator (but not for odd-denominator) values of q in the magnetic flux quanta per plaquette, i.e., $p/q.\mathrm{}$