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

TL;DR

This paper derives a generalized Harper's equation for 2D antiferromagnetically correlated electrons in a magnetic field, providing insights into the density of states and phase diagram, including reentrant magnetization behavior.

Contribution

It introduces a new generalized Harper's equation for correlated electrons and analyzes its implications for magnetization and phase transitions in 2D lattice systems.

Findings

Analytic expression for the density of states.

Predicted phase diagram of staggered magnetization.

Reentrant behavior of magnetization under magnetic field.

Abstract

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, $p/q$.