  We study the time evolution and steady state of the charge current in a
single-impurity Anderson model, using matrix product states techniques. A
nonequilibrium situation is imposed by applying a bias voltage across
one-dimensional tight-binding leads. Focusing on particle-hole symmetry, we
extract current-voltage characteristics from universal low-bias up to high-bias
regimes, where band effects start to play a dominant role. We discuss three
quenches, which after strongly quench-dependent transients yield the same
steady-state current. Among these quenches we identify those favorable for
extracting steady-state observables. The period of short-time oscillations is
shown to compare well to real-time renormalization group results for a simpler
model of spinless fermions. We find indications that many-body effects play an
important role at high-bias voltage and finite bandwidth of the metallic leads.
The growth of entanglement entropy after a certain time scale (proportional to
the inverse of Delta) is the major limiting factor for calculating the time
evolution. We show that the magnitude of the steady-state current positively
correlates with entanglement entropy. The role of high-energy states for the
steady-state current is explored by considering a damping term in the time
evolution.
