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We announce and sketch the rigorous proof of a new kind of anomalous (orsub-ballistic) Lieb-Robinson bound for an isotropic XY chain in aquasi-periodic transversal magnetic field. By "anomalous", we mean that theusual effective light cone defined by $|x|\leq v|t|$ is replaced by the region$|x|\leq v|t|^\alpha$ for some $0<\alpha<1$. In fact, we can characterizeexactly the values of $\alpha$ for which this holds as those exceeding theupper transport exponent $\alpha_u^+$ of an appropriate one-body discreteSchr\"odinger operator. Previous study has produced a good amount ofquantitative information on $\alpha_u^+$.  The result is obtained by mapping to free fermions, obtaining good dynamicalbounds on the one-body level by adapting techniques developed by Damanik,Gorodetski, Tcheremchantsev, and Yessen and then "pulling back" these boundsthrough the non-local Jordan-Wigner transformation, following an idea of Hamza,Sims, and Stolz. To our knowledge, this is the first rigorous derivation ofanomalous many-body transport.  We also explain why our method does not extend to yield anomalous LR boundsof power-law type if one replaces the quasi-periodic field by a random dimerfield.

New Anomalous Lieb-Robinson Bounds in Quasi-Periodic XY Chains