A compellingly simple proof of the speed of sound for interacting bosons

• URL: http://arxiv.org/abs/2601.00111v1
• Date: Wed, 31 Dec 2025 21:06:32 GMT
• Title: A compellingly simple proof of the speed of sound for interacting bosons
• Authors: J. Eisert,
• Abstract summary: Lieb-Robinson bounds state that locally interacting Hamiltonians with finite-dimensional constituents always exhibit such a finite group velocity.<n>It had been a long-standing open question whether interacting bosonic systems also feature finite speeds of sound in information and particle propagation.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: On physical grounds, one expects locally interacting quantum many-body systems to feature a finite group velocity. This intuition is rigorously underpinned by Lieb-Robinson bounds that state that locally interacting Hamiltonians with finite-dimensional constituents on suitably regular lattices always exhibit such a finite group velocity. This also implies that causality is always respected by the dynamics of quantum lattice models. It had been a long-standing open question whether interacting bosonic systems also feature finite speeds of sound in information and particle propagation, which was only recently resolved. This work proves a strikingly simple such bound for particle propagation - shown in literally a few elementary, yet not straightforward, lines - for generalized Bose-Hubbard models defined on general lattices, proving that appropriately locally perturbed stationary states feature a finite speed of sound in particle numbers.

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