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… 

On Polynomial Lieb–Robinson Bounds for the XY Chain in a Decaying Random Field

We consider the isotropic XY quantum spin chain in a random external field in the z direction, with single site distributions given by i.i.d. random variables times the critical decaying envelope

On Transport Properties of Isotropic Quasiperiodic XY Spin Chains

AbstractWe consider isotropic XY spin chains whose magnetic potentials are quasiperiodic and the effective one-particle Hamiltonians have absolutely continuous spectra. For a wide class of such XY

On the relation between strong ballistic transport and exponential dynamical localization

We establish strong ballistic transport for a family of discrete quasiperiodic Schr\"odinger operators as a consequence of exponential dynamical localization for the dual family. The latter has been,

Ballistic transport for one-dimensional quasiperiodic Schr\"odinger operators

In this paper, we show that one-dimensional discrete multi-frequency quasiperiodic Schrodinger operators with smooth potentials demonstrate ballistic motion on the set of energies on which the

Maximal Speed for Macroscopic Particle Transport in the Bose-Hubbard Model.

The Lieb-Robinson bound asserts the existence of a maximal propagation speed for the quantum dynamics of lattice spin systems. Such general bounds are not available for most bosonic lattice gases due

Mathematical Results on Quantum Many-body Physics

The collective behavior exhibited by a large number of microscopic quantum particles is at the heart of some of the most striking phenomena in condensed matter physics such as Bose-Einstein

Maximal Speed of Propagation in Open Quantum Systems

. We prove a maximal velocity bound for the dynamics of Markovian open quantum systems. The dynamics are described by one-parameter semigroups of quantum channels satisfying the von Neumann-Lindblad

Fractalized magnon transport on the quasicrystal with enhanced stability

Magnonics has been receiving significant attention in magnetism and spintronics because of its premise for devices using spin current carried by magnons, quanta of spin-wave excitations of a



New anomalous Lieb-Robinson bounds in quasiperiodic XY chains.

To the knowledge, this is the first rigorous derivation of anomalous quantum many-body transport and bounds with power-law tails for a random dimer field.

The Fibonacci Hamiltonian

We consider the Fibonacci Hamiltonian, the central model in the study of electronic properties of one-dimensional quasicrystals, and establish relations between its spectrum and spectral

Dynamical Bounds for Sturmian Schrödinger Operators

Abstract The Fibonacci Hamiltonian, that is a Schrodinger operator associated to a Sturmian potential with respect to the golden number has been investigated intensively in recent years. Damanik and

Upper bounds in quantum dynamics

Of course, the case of main interest is where H is given by L2(Rd) or ?2(Zd), H is a Schr?dinger operator of the form ? A + V, and ip(0) is a localized wavepacket. Under the time evolution (1), the

Uniform Spectral Properties of One-Dimensional Quasicrystals, III. α-Continuity

Abstract: We study the spectral properties of one-dimensional whole-line Schrödinger operators, especially those with Sturmian potentials. Building upon the Jitomirskaya–Last extension of the

Upper Bounds On Wavepacket Spreading For Random Jacobi Matrices

A method is presented for proving upper bounds on the moments of the position operator when the dynamics of quantum wavepackets is governed by a random (possibly correlated) Jacobi matrix. As an

The finite group velocity of quantum spin systems

AbstractIt is shown that if Φ is a finite range interaction of a quantum spin system,τtΦ the associated group of time translations, τx the group of space translations, andA, B local observables, then

Delocalization in Random Polymer Models

Abstract: A random polymer model is a one-dimensional Jacobi matrix randomly composed of two finite building blocks. If the two associated transfer matrices commute, the corresponding energy is