Interplay of Soundcone and Supersonic Propagation in Lattice Models with Power Law Interactions

Abstract

We study the spreading of correlations and other physical quantities in quantum lattice models with interactions or hopping decaying like $r^{-\alpha }$ with the distance $r$. Our focus is on exponents $\alpha$ 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. We present analytical and numerical results, providing a comprehensive picture of spatio-temporal propagation. Lieb-Robinson-type bounds are extended to strongly long-range interactions where $\alpha$ 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 $\alpha <2$ 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.

20 pages, 8 figures

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Cited by in corpus (9)

• Long-range interacting quantum systems
• The Lieb-Robinson light cone for power-law interactions
• Out-of-equilibrium dynamics of quantum many-body systems with long-range interactions
• Generalized Higgs mechanism in long-range interacting quantum systems
• Suppression of heating by long-range interactions in periodically driven spin chains
• Long-range interacting systems are locally non-interacting
• Impact of dephasing on non-equilibrium steady-state transport in fermionic chains with long-range hopping
• Delocalized Excitation Transfer in Open Quantum Systems with Long-Range Interactions
• Expediting quantum state transfer through the long-range extended XY model