We study the concentration and uniqueness of standing waves associated with the constraint minimization problems for the nonlinear Hartree type equations with homogeneous potentials and fractional Laplacian. This class of equations is an effective model to describe the fractional quantum mechanics with a convolution perturbation. By making full use of the Bessel kernel and adopting the iterative process, we establish the \(L^{\infty }\) -estimates and decay properties of the solutions to the fractional Hartree equations. Based on the above basic conclusions, we establish the concentration and uniqueness of the constraint minimizers by exploring some fine energy estimates and studying some uniform regularity, while establishing local Pohozăev identity and overcoming the blow-up estimates to the nonlocal operator \((-\Delta )^{s}\) . Compared with the classical local elliptic problems, we encounter some new difficulties because of the nonlocal nature of the fractional Laplace. One of the main difficulties is that the decay estimates of the sequences of solutions to the nonlocal problems at infinity are different from those in the case of the classical local problems. Another difficulty is that we have to consider the corresponding harmonic extension problems to construct the Pohozăev identity, which will cause us to have to estimate several kinds of integrals that never appear in the classic local problems. In addition, the presence of the potential \(|x|^{2}\) and the Hartree term \(|x|^{2s-3}*u^{2}\) will affect the blow-up frequency of the minimizers, and we have to control s to achieve the optimal blow-up speed.
