Enhanced Lieb-Robinson bounds for commuting long-range interactions
arXiv:2411.19241 · doi:10.1063/5.0252675
Abstract
Recent works have revealed the intricate effect of long-range interactions on information transport in quantum many-body systems: In spatial dimensions, interactions decaying as a power-law with exhibit a Lieb-Robinson bound (LRB) with a linear light cone and the threshold is sharp in general. Here, we observe that mutually commuting, long-range interactions satisfy an enhanced LRB of the form for any , and this scaling is sharp. In particular, the linear light cone occurs at 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.
v2: changed presentation of operator localization LRB; added reference for LRB with to Figure 1; fixed typos. v3: added result on sharpness of the bounds; fixed typos. v4: updated references; fixed typos; (final version corresponding to the published article)
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