# Persistence of locality in systems with power-law interactions.

@article{Gong2014PersistenceOL, title={Persistence of locality in systems with power-law interactions.}, author={Zhe-Xuan Gong and Michael Foss-Feig and Spyridon Michalakis and Alexey V. Gorshkov}, journal={Physical review letters}, year={2014}, volume={113 3}, pages={ 030602 } }

Motivated by recent experiments with ultracold matter, we derive a new bound on the propagation of information in D-dimensional lattice models exhibiting 1/r^{α} interactions with α>D. The bound contains two terms: One accounts for the short-ranged part of the interactions, giving rise to a bounded velocity and reflecting the persistence of locality out to intermediate distances, whereas the other contributes a power-law decay at longer distances. We demonstrate that these two contributions not…

## 83 Citations

Dynamics of long-range interacting quantum spin systems

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In this thesis we study the time evolution of correlation functions in quantum lattice models in the presence of long-range interactions or hopping decaying asymptotically as a power law. For a large…

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While the interactions are long-range, their effect on information spreading is asymptotically negligible as long as $\alpha>1$, which directly implies that all previously obtained rigorous bounds on information spread in long- range interacting systems are not tight, and thus could be improved.

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It is conjecture that the gap between the results from the linear response theory and the Magnus-like expansion does not have physical implications, but is, rather, due to the lack of tight Lieb-Robinson bounds for power-law interactions.

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- 2014

This work applies a variable-range Ising spin chain Hamiltonian and aVariable-range XY spin chainHamiltonian to a far-from-equilibrium quantum many-body system and observes its time evolution, determining the spatial and time-dependent correlations, extracting the shape of the light cone and measuring the velocity with which correlations propagate through the system.

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Long-range interactions allow far-distance quantum correlations to build up very fast. Nevertheless, numerical simulations demonstrated a dramatic slowdown of entanglement entropy growth after a…

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