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 $|x|\le v|t|$, we obtain $|x|\le v|t{|}^{\alpha }$ for some $0<\alpha <1$. We can characterize the allowed values of $\alpha$ exactly as those exceeding the upper transport exponent ${\alpha }_u^{+}$ of a one-body Schrödinger 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.

• Received 13 August 2014

DOI:https://doi.org/10.1103/PhysRevLett.113.127202