Enhanced Lieb-Robinson bounds for commuting long-range interactions

• URL: http://arxiv.org/abs/2411.19241v2
• Date: Mon, 09 Dec 2024 15:28:21 GMT
• Title: Enhanced Lieb-Robinson bounds for commuting long-range interactions
• Authors: Marius Lemm, Tom Wessel,
• Abstract summary: We show the intricate effect of long-range interactions on information transport in quantum many-body systems. Part of our motivation stems from quantum error-correcting codes.
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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 $r^{-\alpha}$ with $\alpha > 2D+1$ 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 $\alpha > 0$. 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.

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