Maximal Speed for Macroscopic Particle Transport in the Bose-Hubbard Model

Jérémy Faupin, Marius Lemm, and Israel Michael Sigal
Phys. Rev. Lett. 128, 150602 – Published 12 April 2022
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Abstract

The Lieb-Robinson bound asserts the existence of a maximal propagation speed for the quantum dynamics of lattice spin systems. Such general bounds are not available for most bosonic lattice gases due to their unbounded local interactions. Here we establish for the first time a general ballistic upper bound on macroscopic particle transport in the paradigmatic Bose-Hubbard model. The bound is the first to cover a broad class of initial states with positive density including Mott states, which resolves a longstanding open problem. It applies to Bose-Hubbard–type models on any lattice with not too long-ranged hopping. The proof is rigorous and rests on controlling the time evolution of a new kind of adiabatic spacetime localization observable via iterative differential inequalities.

  • Figure
  • Received 8 October 2021
  • Accepted 18 February 2022

DOI:https://doi.org/10.1103/PhysRevLett.128.150602

© 2022 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & Thermodynamics

Authors & Affiliations

Jérémy Faupin1,*, Marius Lemm2,†, and Israel Michael Sigal3,‡

  • 1Institut Elie Cartan de Lorraine, Université de Lorraine, 57045 Metz Cedex 1, France
  • 2Department of Mathematics, University of Tübingen, 72076 Tübingen, Germany
  • 3Department of Mathematics, University of Toronto, Toronto, M5S 2E4 Ontario, Canada

  • *jeremy.faupin@univ-lorraine.fr
  • marius.lemm@uni-tuebingen.de
  • im.sigal@utoronto.ca

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Issue

Vol. 128, Iss. 15 — 15 April 2022

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