The Lieb-Robinson light cone for power-law interactions

TL;DR

This paper establishes the fundamental speed limits for information propagation in quantum systems with power-law interactions, extending Lieb-Robinson bounds to a broad class of long-range interacting systems.

Contribution

It provides a definitive Lieb-Robinson bound for power-law interactions with decay exponent greater than twice the dimension, resolving a long-standing open problem.

Findings

Information propagates at least as fast as r^{min{1, α-2d}}

Bounds are tight, saturating known state transfer protocols

Closes decades-long search for optimal bounds in long-range systems

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.