Improving the Lieb-Robinson bound for long-range interactions

TL;DR

This paper enhances the Lieb-Robinson bound for quantum systems with long-range power-law interactions, revealing that information propagation speed increases polynomially over time, unlike the finite speed in short-range systems.

Contribution

It provides an improved Lieb-Robinson bound applicable to long-range interactions and demonstrates the polynomial growth of information propagation speed.

Findings

Group velocity grows polynomially in time for long-range systems

Short-range systems maintain finite group velocity

Enhanced bounds improve understanding of quantum information spread

Abstract

We improve the Lieb-Robinson bound for a wide class of quantum many-body systems with long-range interactions decaying by power law. As an application, we show that the group velocity of information propagation grows by power law in time for such systems, whereas systems with short-range interactions exhibit a finite group velocity as shown by Lieb and Robinson.