On Anomalous Lieb-Robinson Bounds for the Fibonacci XY Chain
  We rigorously prove a new kind of anomalous (or sub-ballistic) Lieb-Robinson bound for the isotropic XY chain with Fibonacci external magnetic field at arbitrary coupling. It is anomalous in that the usual exponential decay in $x-vt$ is replaced by exponential decay in $x-vt^\alpha$ with $0<\alpha<1$. In fact, we can characterize the values of $\alpha$ for which such a bound holds as those exceeding $\alpha_u^+$, the upper transport exponent of the one-body Fibonacci Hamiltonian. Following the approach of \cite{HSS11}, we relate Lieb-Robinson bounds to dynamical bounds for the one-body Hamiltonian corresponding to the XY chain via the Jordan-Wigner transformation; in our case the one-body Hamiltonian with Fibonacci potential. We can bound its dynamics by adapting techniques developed in \cite{DT07, DT08, D05, DGY} to our purposes.   We also explain why our method does not extend to yield anomalous Lieb-Robinson bounds of power-law type for the random dimer model. 
David Damanik (Rice University), Marius Lemm (California Institute of   Technology), Milivoje Lukic (Rice University), Willi...
math-ph math.DS math.MP math.SP quant-ph