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

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 $t^{d+\epsilon}$.

32 pages, 1 figure. final version to appear in PAFA special issue dedicated to Barry Simon on the occasion of his 80th birthday

Mathematical Physics (math-ph); Analysis of PDEs (math.AP); Quantum Physics (quant-ph)

arXiv:2603.26209 [math-ph]

(or arXiv:2603.26209v2 [math-ph] for this version)

https://doi.org/10.48550/arXiv.2603.26209 Focus to learn more arXiv-issued DOI via DataCite

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.