  We develop an effective extended Hubbard model to describe the low-energy
electronic properties of the twisted bilayer graphene. By using the Bloch
states in the effective continuum model and with the aid of the maximally
localized algorithm, we construct the Wannier orbitals and obtain an effective
tight-binding model on the emergent honeycomb lattice. We found the Wannier
state takes a peculiar three-peak form in which the amplitude maxima are
located at the triangle corners surrounding the center. We estimate the direct
Coulomb interaction and the exchange interaction between the Wannier states. At
the filling of two electrons per super cell, in particular, we find an
unexpected coincidence in the direct Coulomb energy between a charge-ordered
state and a homogeneous state, which would possibly lead to an unconventional
many-body state.
