Phase diagram for the Harper model of the honeycomb lattice

TL;DR

This paper investigates the phase diagram of the Harper model on a honeycomb lattice under magnetic field, revealing three phases and analyzing the effects of next nearest neighbor hopping on eigenstate localization.

Contribution

It provides a detailed phase diagram for the Harper model on a honeycomb lattice and explores the impact of extended hopping terms on phase structure.

Findings

Identified three distinct phases: two metallic and one insulating.

Used multifractal analysis and entropy measures to characterize phases.

Showed that next nearest neighbor hopping introduces a mobility edge.

Abstract

The Harper equation arising out of a tight-binding model of electrons on a honeycomb lattice subject to a uniform magnetic field perpendicular to the plane is studied. Contrasting and complementary approaches involving von Neumann entropy, fidelity, fidelity susceptibility, multifractal analysis are employed to characterize the phase diagram. The phase diagram consists of three phases: two metallic phases and an insulating phase. A variant model where next nearest neighbor hopping is included, exhibits a mobility edge and does not allow for a simple single phase diagram characterizing all the eigenstates.