On the quantum dynamics of long-ranged Bose-Hubbard Hamiltonians

• URL: http://arxiv.org/abs/2505.01786v1
• Date: Sat, 03 May 2025 11:07:23 GMT
• Title: On the quantum dynamics of long-ranged Bose-Hubbard Hamiltonians
• Authors: Marius Lemm, Carla Rubiliani, Jingxuan Zhang,
• Abstract summary: We study the quantum dynamics generated by Bose-Hubbard Hamiltonians with long-ranged (power law) terms.<n>To handle the long-ranged and unbounded terms, we further develop the multiscale ASTLO (adiabatic space time localization observables) method introduced in our recent work.
• Score: 3.3386099307080723
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We study the quantum dynamics generated by Bose-Hubbard Hamiltonians with long-ranged (power law) terms. We prove two ballistic propagation bounds for suitable initial states: (i) A bound on all moments of the local particle number for all power law exponents $\alpha>d+1$ in $d$ dimensions, the sharp condition. (ii) The first thermodynamically stable Lieb-Robinson bound (LRB) for these Hamiltonians. To handle the long-ranged and unbounded terms, we further develop the multiscale ASTLO (adiabatic space time localization observables) method introduced in our recent work [arXiv:2310.14896].

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