The classical Lieb-Robinson bounds provide control over the speed of
propagation in quantum spin systems. In analogy to relativistic systems,
they establish a ``light cone'' $x \leq vt$ outside of which commutators
of initially localized observables are exponentially small. We consider an
XY spin chain in a quasiperiodic magnetic field and prove a new anomalous
Lieb-Robinson bound which features the modified light cone $x \leq
vt^\alpha$ for some $0<\alpha<1$. In fact, we can characterize $\alpha$
exactly as the upper transport exponent of a one-body Schr\"odinger
operator. This may be interpreted as a rigorous proof of anomalous quantum
many-body transport. Joint work with David Damanik, Milivoje Lukic and
William Yessen.