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arXiv · 2411.19241

Enhanced Lieb-Robinson bounds for commuting long-range interactions

Marius Lemm·Tom Wessel
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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 $r^{-α}$ with $α> 2 D+1$ 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 $t \, r^{-α}$ for any $α>0$, and this scaling is sharp. In particular, the linear light cone occurs at $α= 1$ 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.

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Marius Lemm, Tom Wessel. 2025-09-22. Enhanced Lieb-Robinson bounds for commuting long-range interactions. https://doi.org/10.1063/5.0252675

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