Trotter product formulae for $*$-automorphisms of quantum lattice systems

We consider the dynamics $tmapstotau_t$ of an infinite quantum lattice system that is generated by a local interaction. If the interaction decomposes into a finite number of terms that are themselves local interactions, we show that $tau_t$ can be efficiently approximated by a product of $n$ automorphisms, each of them being an alternating product generated by the individual terms. For any integer $m$, we construct a product formula (in the spirit of Trotter) such that the approximation error scales as $n^{-m}$. We do so in the strong topology of the operator algebra, namely by approximating $tau_t(O)$ for sufficiently localized observables $O$.