On Anomalous Lieb-Robinson Bounds for the Fibonacci XY Chain

  title={On Anomalous Lieb-Robinson Bounds for the Fibonacci XY Chain},
  author={David Damanik and Marius Lemm and Milivoje Luki'c and William N. Yessen},
  journal={arXiv: Mathematical Physics},
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… 
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