Caltech/UCLA Joint Analysis Seminar

Abstract: The well known Lieb-Robinson bounds provide control over the speed of information propagation in quantum spin systems. Similarly 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.