  We characterize the dynamics of the finite time blow up solutions with
minimal mass for the focusing mass critical Hartree equation with
$H^1(\mathbb{R}^4)$ data and $L^2(\mathbb{R}^4)$ data, where we make use of the
refined Gagliardo-Nirenberg inequality of convolution type and the profile
decomposition. Moreover, we also analyze the mass concentration phenomenon of
such blow up solutions.
