  We consider single-particle properties in the one-dimensional repulsive
Hubbard model at commensurate fillings in the metallic phase. We determine the
real-time evolution of the retarded Green's function by matrix-product state
methods. We find that at sufficiently late times the numerical results are in
good agreement with predictions of nonlinear Luttinger liquid theory. We argue
that combining the two methods provides a way of determining the
single-particle spectral function with very high frequency resolution.
