Spread of Correlations in Long-Range Interacting Quantum Systems

P. Hauke and L. Tagliacozzo
Phys. Rev. Lett. 111, 207202 – Published 12 November 2013
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Abstract

The nonequilibrium response of a quantum many-body system defines its fundamental transport properties and how initially localized quantum information spreads. However, for long-range-interacting quantum systems little is known. We address this issue by analyzing a local quantum quench in the long-range Ising model in a transverse field, where interactions decay as a variable power law with distance rα, α>0. Using complementary numerical and analytical techniques, we identify three dynamical regimes: short-range-like with an emerging light cone for α>2, weakly long range for 1<α<2 without a clear light cone but with a finite propagation speed of almost all excitations, and fully nonlocal for α<1 with instantaneous transmission of correlations. This last regime breaks generalized Lieb-Robinson bounds and thus locality. Numerical calculation of the entanglement spectrum demonstrates that the usual picture of propagating quasiparticles remains valid, allowing an intuitive interpretation of our findings via divergences of quasiparticle velocities. Our results may be tested in state-of-the-art trapped-ion experiments.

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  • Received 7 May 2013

DOI:https://doi.org/10.1103/PhysRevLett.111.207202

© 2013 American Physical Society

Authors & Affiliations

P. Hauke1,2,* and L. Tagliacozzo3,†

  • 1Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, A-6020 Innsbruck, Austria
  • 2Institute for Theoretical Physics, University of Innsbruck, A-6020 Innsbruck, Austria
  • 3ICFO—Institut de Ciencies Fotoniques, Avenue Carl Friedrich Gauss, 3 08860 Castelldefels, Barcelona, Spain

  • *philipp.hauke@uibk.ac.at
  • luca.tagliacozzo@icfo.es

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Issue

Vol. 111, Iss. 20 — 15 November 2013

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