Enhanced Lieb-Robinson bounds for commuting long-range interactions

TL;DR

This paper establishes improved Lieb-Robinson bounds for commuting long-range quantum interactions, showing faster information propagation and sharper bounds than previously known, with implications for quantum error correction and ground state correlations.

Contribution

It introduces enhanced Lieb-Robinson bounds for commuting long-range interactions, demonstrating sharper and more general bounds than prior results, including for stretched exponential decay.

Findings

Enhanced bounds for commuting interactions with power-law decay

Linear light cone at decay exponent mbda=1 in any dimension

Improved bounds on ground state correlations and local perturbations

Abstract

Recent works have revealed the intricate effect of long-range interactions on information transport in quantum many-body systems: In $D$ spatial dimensions, interactions decaying as a power-law $r^{-\alpha}$ with $\alpha > 2 D+1$ exhibit a Lieb-Robinson bound (LRB) with a linear light cone and the threshold $2D +1$ is sharp in general. Here, we observe that mutually commuting, long-range interactions satisfy an enhanced LRB of the form $t \, r^{-\alpha}$ for any $\alpha>0$, and this scaling is sharp. In particular, the linear light cone occurs at $\alpha = 1$ in any dimension. Part of our motivation stems from quantum error-correcting codes. As applications, we derive enhanced bounds on ground state correlations and an enhanced local perturbations perturb locally (LPPL) principle for which we adapt a recent subharmonicity argument of Wang-Hazzard. Similar enhancements hold for commuting interactions with stretched exponential decay.