Enhanced Lieb-Robinson bounds for commuting long-range interactions
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866918145198915584 |
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| author | Lemm, Marius Wessel, Tom |
| author_facet | Lemm, Marius Wessel, Tom |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_19241 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Enhanced Lieb-Robinson bounds for commuting long-range interactions Lemm, Marius Wessel, Tom Mathematical Physics Quantum Physics 81Q35, 81Q80, 91V70 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. |
| title | Enhanced Lieb-Robinson bounds for commuting long-range interactions |
| topic | Mathematical Physics Quantum Physics 81Q35, 81Q80, 91V70 |
| url | https://arxiv.org/abs/2411.19241 |