Phase diagram for the Harper model of the honeycomb lattice

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, and multifractal analysis are employed to characterize the phase diagram. Remarkably even in the absence of the quasi-periodic on-site potential term, the Hamiltonian allows for a metal-insulator transition. 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.