  We have studied the revival of Hofstadter butterfly due to the competition
between disorder and electronic interaction using mean field approximation of
unrestricted Hartree Fock method at zero temperature for two dimensional square
and honeycomb lattices. Interplay of disorder and electronic correlation to
nullify each other is corroborated by the fact that honeycomb lattice needs
more strength of electronic correlation owing to its less co-ordination number
which enhances the effect of disorder. The extent of revival of the butterfly
is better in square than honeycomb lattice due to higher coordination number.
The effect of disorder and interaction is also investigated to study
entanglement entropy and entanglement spectrum. It has been observed that for
the square lattice, area law of entanglement entropy is violated for
intermediate strength magnetic and magnitude of such departure from area law
depends on disorder and interaction as well. However such departure from area
law is absence for honeycomb lattice. Moreover the entanglement spectrum for
square lattice does have the symmetry of original Hofstadter butterfly and this
symmetry is destroyed in the presence of disorder. The interaction opens up a
gap in the entanglement spectrum as well. For the honeycomb lattice, the
entanglement spectrum forms a continuous band without any symmetry and its
feature is mostly unchanged in the presence of disorder as well as interaction.
