### Abstract

We say that a quantum spin system is dynamically localized if the time-evolution of local observables satisfies a zero-velocity Lieb-Robinson bound. In terms of this definition we have the following main results: First, for general systems with short range interactions, dynamical localization implies exponential decay of ground state correlations, up to an explicit correction. Second, the dynamical localization of random xy spin chains can be reduced to dynamical localization of an effective one-particle Hamiltonian. In particular, the isotropic xy chain in random exterior magnetic field is dynamically localized.

Original language | English (US) |
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Pages (from-to) | 215-239 |

Number of pages | 25 |

Journal | Communications in Mathematical Physics |

Volume | 315 |

Issue number | 1 |

DOIs | |

State | Published - Sep 1 2012 |

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

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## Cite this

Hamza, E., Sims, R., & Stolz, G. (2012). Dynamical Localization in Disordered Quantum Spin Systems.

*Communications in Mathematical Physics*,*315*(1), 215-239. https://doi.org/10.1007/s00220-012-1544-6