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arXiv · 1407.4924

On Anomalous Lieb-Robinson Bounds for the Fibonacci XY Chain

David Damanik·Marius Lemm·Milivoje Lukic·William Yessen
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Abstract

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 $x-vt^α$ with $0<α<1$. In fact, we can characterize the values of $α$ for which such a bound holds as those exceeding $α_u^+$, 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.

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David Damanik, Marius Lemm, Milivoje Lukic, William Yessen. 2016-04-14. On Anomalous Lieb-Robinson Bounds for the Fibonacci XY Chain. https://arxiv.org/abs/1407.4924

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