Interplay of soundcone and supersonic propagation in lattice models with power law interactions

Storch, David-Maximilian ; Van den Worm, Mauritz ; Kastner, Michael (2015-06-16)

CITATION: Storch, D-M., Van den Worm, M. & Kastner, M. 2015. Interplay of soundcone and supersonic propagation in lattice models with power law interactions. New Journal of Physics, 17:063021, doi:10.1088/1367-2630/17/6/063021.

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Westudy the spreading of correlations and other physical quantities in quantum lattice models with interactions or hopping decaying like r−α with the distance r.Our focus is on exponents α between 0 and 6, where the interplay of long- and short-range features gives rise to a complex phenomenology and interesting physical effects, and which is also the relevant range for experimental realizations with cold atoms, ions, or molecules.Wepresent analytical and numerical results, providing a comprehensive picture of spatio-temporal propagation. Lieb–Robinson-type bounds are extended to strongly long-range interactions where α is smaller than the lattice dimension, and we report particularly sharp bounds that are capable of reproducing regimes with soundcone as well as supersonic dynamics. Complementary lower bounds prove that faster-than-soundcone propagation occurs for α < 2 in any spatial dimension, although cone-like features are shown to also occur in that regime. Our results provide guidance for optimizing experimental efforts to harness long-range interactions in a variety of quantum information and signaling tasks.

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