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arXiv · 2603.26209

Lieb-Robinson bounds for Bose-Hubbard Hamiltonians: A review with a simplified proof

Marius Lemm·Carla Rubiliani
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Abstract

We review recent progress on state-dependent Lieb--Robinson bounds for Bose--Hubbard Hamiltonians. In particular, Kuwahara, Vu, and Saito established that, for general bounded-density initial states, the Lieb--Robinson velocity is bounded by $t^{d-1}$ for large times, where $d$ denotes the lattice dimension. We present a shorter proof of the weaker, but still polynomial velocity bound $t^{d+\epsilon}$.

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Marius Lemm, Carla Rubiliani. 2026-03-27. Lieb-Robinson bounds for Bose-Hubbard Hamiltonians: A review with a simplified proof. https://arxiv.org/abs/2603.26209

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