New Anomalous Lieb-Robinson Bounds in Quasiperiodic XY Chains

We announce and sketch the rigorous proof of a new kind of anomalous (or sub-ballistic) Lieb-Robinson (LR) bound for an isotropic XY chain in a quasiperiodic transversal magnetic field. Instead of the usual effective light cone vertical bar x vertical bar <= nu vertical bar t vertical bar, we obtain vertical bar x vertical bar <= nu vertical bar t vertical bar(alpha) for some 0 < alpha < 1. We can characterize the allowed values of a exactly as those exceeding the upper transport exponent alpha(+)(u) of a one-body Schrodinger operator. To our knowledge, this is the first rigorous derivation of anomalous quantum many-body transport. We also discuss anomalous LR bounds with power-law tails for a random dimer field.