The Lieb-Robinson light cone for power-law interactions
- URL: http://arxiv.org/abs/2103.15828v1
- Date: Mon, 29 Mar 2021 18:00:00 GMT
- Title: The Lieb-Robinson light cone for power-law interactions
- Authors: Minh C. Tran, Andrew Y. Guo, Christopher L. Baldwin, Adam Ehrenberg,
Alexey V. Gorshkov, Andrew Lucas
- Abstract summary: We show that information takes time at least $rmin1, alpha-2d$ to propagate a distance$r$.
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.
- Score: 0.5592394503914488
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- 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 $1/r^\alpha$ at distance $r$? Here, we
present a definitive answer to this question for all exponents $\alpha>2d$ and
all spatial dimensions $d$. Schematically, information takes time at least
$r^{\min\{1, \alpha-2d\}}$ to propagate a distance~$r$. 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.
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