Lieb-Robinson Light Cones in Long-Range Bosonic Systems
Abstract
Lieb-Robinson bounds formulate emergent causality in quantum many-body dynamics. In this Letter, we study interacting bosonic systems with long-range interactions, in which both the standard assumptions of short-range interactions and uniformly bounded local energy scales are absent. We derive upper and lower bounds whose effective light-cone exponents are governed by a nontrivial interplay between the decay exponent α and the bosonic interaction order p. The propagation protocol concentrates bosons within blocks, creating a mediating sublattice with amplified interactions. For p≥4 and 2d<α≤2d+1, the resulting exponents coincide, determining the optimal leading light-cone power. The upper bound includes α=2d+1 with arbitrarily small exponent loss, using a fixed-k extension of the bounded-interaction result. Our results reveal that the interplay between long-range couplings and unbounded bosonic degrees of freedom gives rise to a richer light-cone structure than in either long-range bounded systems or short-range bosonic systems alone.
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BibTeX
@misc{rubiliani2026liebrobinson,
title = {{Lieb-Robinson Light Cones in Long-Range Bosonic Systems}},
author = {Carla Rubiliani and Cheng Shang and Tomotaka Kuwahara},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.00776},
eprint = {2611.00776},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.00776},
}
RIS
TY - UNPB
TI - Lieb-Robinson Light Cones in Long-Range Bosonic Systems
AU - Carla Rubiliani
AU - Cheng Shang
AU - Tomotaka Kuwahara
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.00776
UR - https://arxiv.org/abs/2611.00776
AB - Lieb-Robinson bounds formulate emergent causality in quantum many-body dynamics. In this Letter, we study interacting bosonic systems with long-range interactions, in which both the standard assumptions of short-range interactions and uniformly bounded local energy scales are absent. We derive upper and lower bounds whose effective light-cone exponents are governed by a nontrivial interplay between the decay exponent α and the bosonic interaction order p. The propagation protocol concentrates bosons within blocks, creating a mediating sublattice with amplified interactions. For p≥4 and 2d<α≤2d+1, the resulting exponents coincide, determining the optimal leading light-cone power. The upper bound includes α=2d+1 with arbitrarily small exponent loss, using a fixed-k extension of the bounded-interaction result. Our results reveal that the interplay between long-range couplings and unbounded bosonic degrees of freedom gives rise to a richer light-cone structure than in either long-range bounded systems or short-range bosonic systems alone.
ER -