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  • Letter
  • Open Access

Spreading of correlations and entanglement in the long-range transverse Ising chain

J. T. Schneider1,*, J. Despres1, S. J. Thomson1, L. Tagliacozzo2,3, and L. Sanchez-Palencia1

  • 1CPHT, CNRS, Ecole Polytechnique, IP Paris, F-91128 Palaiseau, France
  • 2Department of Physics and SUPA, University of Strathclyde, Glasgow G4 0NG, United Kingdom
  • 3Departament de Física Quàntica i Astrofísica and Institut de Ciències del Cosmos (ICCUB), Universitat de Barcelona, Martí i Franquès 1, E-08028 Barcelona, Catalonia, Spain

  • *Corresponding author: jan.schneider@polytechnique.edu
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Phys. Rev. Research 3, L012022 – Published 5 March, 2021

DOI: https://doi.org/10.1103/PhysRevResearch.3.L012022

Abstract

Whether long-range interactions allow for a form of causality in nonrelativistic quantum models remains an open question with far-reaching implications for the propagation of information and thermalization processes. Here, we study the out-of-equilibrium dynamics of the one-dimensional transverse Ising model with algebraic long-range exchange coupling. Using a state of the art tensor-network approach, complemented by analytic calculations and considering various observables, we show that a weak form of causality emerges, characterized by nonuniversal dynamical exponents. While the local spin and spin correlation causal edges are sub-ballistic, the causal region has a rich internal structure, which, depending on the observable, displays ballistic or superballistic features. In contrast, the causal region of entanglement entropy is featureless and its edge is always ballistic, irrespective of the interaction range. Our results shed light on the propagation of information in long-range interacting lattice models and pave the way to future experiments, which are discussed.

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Phys. Rev. Research 3, L012022– Published 5 March, 2021
  • Received 23 November 2020
  • Accepted 28 January 2021
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