  In this paper, we consider the asymptotic behaviors of small solutions to the
semi-relativistic Hartree equations in two dimension. The nonlinear term is
convolved with the Coulomb potential 1/|x|, and it produces the long-range
interaction in the sense of scattering phenomenon. From this observation, one
anticipates that small solutions converge to a modified scattering states,
although they decay as linear solutions. We show the global well-posedness and
the modified scattering for small solutions in weighted Sobolev spaces. Our
proof follows a road map of exploiting the space-time resonance developed by
Germain, Masmoudi, and Shatah. Compared to the result in three dimensional case
by Pusateri, weaker time decay in two dimension is one of the main obstacles.
