  The recently introduced auxiliary Hamiltonian approach [Balzer K and Eckstein
M 2014 Phys. Rev. B 89 035148] maps the problem of solving the two-time
Kadanoff-Baym equations onto a noninteracting auxiliary system with additional
bath degrees of freedom. While the original paper restricts the discussion to
spatially local self-energies, we show that there exists a rather
straightforward generalization to treat also non-local correlation effects. The
only drawback is the loss of time causality due to a combined singular value
and eigen decomposition of the two-time self-energy, the application of which
inhibits one to establish the self-consistency directly on the time step. For
derivation and illustration of the method, we consider the Hubbard model in one
dimension and study the decay of the Neel state in the weak-coupling regime,
using the local and non-local second-order Born approximation.
