  We present a method to calculate many-body states of interacting carriers in
million atom quantum nanostructures based on atomistic tight-binding
calculations and a combination of iterative selection of configurations and
perturbation theory. This method enables investigations of large excitonic
complexes and multi-electron systems with near full configuration interaction
accuracy, even though only a small subspace of the full many-body Hilbert space
is sampled, thus saving orders of magnitudes in computational resources.
Important advantages of this method are that the convergence is controlled by a
single parameter, the threshold, and that ground and excited states can be
treated on an equal footing. We demonstrate the extreme efficiency of the
method by numerical studies of complexes composed of up to 13 excitons, which
requires filling of states up to the fourth electronic shell. We find that the
method generally converges fast as a function of the threshold, profiting from
a significant enhancement due to the perturbative corrections. The role of the
choice of single-particle basis states is discussed. It is found that the
algorithm converges faster in the Hartree-Fock basis only for highly charged
systems, where Coulomb repulsion dominates. Finally, based on the observation
that second order perturbative energy corrections only depend on off-diagonal
elements of the many-body Hamiltonian, we present a way to accurately calculate
many-body states that requires only a relatively small number of Coulomb matrix
elements.
