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Lieb-Robinson bounds for Bose-Hubbard Hamiltonians: A review with a simplified proof
Marius Lemm, Carla Rubiliani·March 27, 2026
Mathematical Physicsmath.APQuantum Physics
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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 $t^{d+ε}$.