Study of Harper's Equation for the 2-D Systems of Antiferromagnetically Correlated Electrons in an External Magnetic Field

Considering interacting (antiferromagnetically correlated) electrons, we derive a generalized Harper's equation for the square lattice of infinite size. We obtain an analytic expression for the density of states from the newly derived Harper's equation. We present a predicted phase diagram of staggered magnetization in the plane of temperature vs doping rate and discover a possibility of reentrant behavior of the staggered magnetization even in the presence of applied magnetic field. It is shown that below a critical electron correlation strength (Coulomb repulsion) the staggered magnetization in the presence of magnetic field vanishes at an even denominator $q$ value but not at odd $q$ of a given magnetic flux quantum per plaquette, $p/q$.