Lieb-Robinson bounds for Bose-Hubbard Hamiltonians via path expansions

@misc{elgart2026liebrobinson,
  title = {{Lieb-Robinson bounds for Bose-Hubbard Hamiltonians via path expansions}},
  author = {Alexander Elgart and Marius Lemm},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.02263},
  eprint = {2611.02263},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.02263},
}

TY  - UNPB
TI  - Lieb-Robinson bounds for Bose-Hubbard Hamiltonians via path expansions
AU  - Alexander Elgart
AU  - Marius Lemm
PY  - 2026
DA  - 2026/11/01
PB  - arXiv
DO  - 10.48550/arxiv.2611.02263
UR  - https://arxiv.org/abs/2611.02263
AB  - We study the transport properties of Bose-Hubbard-type Hamiltonians. Kuwahara, Vu, and Saito proved sharp bounds on (i) particle transport and (ii) the Lieb-Robinson velocity for initial states with controlled boson density. We provide simpler and shorter proofs for both results using a new set of methods. For (i), boson transport, we use a class of weighted extended particle number operators that directly enables closing the associated differential inequalities. For (ii), the Lieb-Robinson bounds, we develop a bosonic version of the Chen-Lucas path expansion technique and recover the sharp velocity bound t^d−1 up to logarithmic corrections, where d denotes the lattice dimension. We also extend the transport bounds (i) to long-range hopping with a power-law exponent α>d. The range α∈ (d,d+1) corresponds to an algebraic light cone for boson transport and has not been previously covered.
ER  -