English

The Lieb-Robinson light cone for power-law interactions

Quantum Physics 2021-10-20 v1 Quantum Gases

Abstract

The Lieb-Robinson theorem states that information propagates with a finite velocity in quantum systems on a lattice with nearest-neighbor interactions. What are the speed limits on information propagation in quantum systems with power-law interactions, which decay as 1/rα1/r^\alpha at distance rr? Here, we present a definitive answer to this question for all exponents α>2d\alpha>2d and all spatial dimensions dd. Schematically, information takes time at least rmin{1,α2d}r^{\min\{1, \alpha-2d\}} to propagate a distance~rr. As recent state transfer protocols saturate this bound, our work closes a decades-long hunt for optimal Lieb-Robinson bounds on quantum information dynamics with power-law interactions.

Cite

@article{arxiv.2103.15828,
  title  = {The Lieb-Robinson light cone for power-law interactions},
  author = {Minh C. Tran and Andrew Y. Guo and Christopher L. Baldwin and Adam Ehrenberg and Alexey V. Gorshkov and Andrew Lucas},
  journal= {arXiv preprint arXiv:2103.15828},
  year   = {2021}
}
R2 v1 2026-06-24T00:39:43.580Z