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arXiv:2011.11296 · Physical Review Research

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

J. T. Schneider, Julien Despres, S. J. Thomson, Luca Tagliacozzo, Laurent Sanchez-Palencia

Published Mar 5, 2021• 38 citations
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Abstract

This work analyzes the nonequilibrium dynamics of a long-range quantum system. The authors show that, while the spreading of spin correlations depends crucially on the interaction range, the propagation of entanglement remains almost independent of it.
DOI
10.1103/physrevresearch.3.l012022

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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 ∝r(-α), 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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