The Lieb-Robinson condition and the Fr\'echet topology
Mathematical Physics
2025-12-03 v1 math.MP
Abstract
We define various notions of locality for *-automorphisms of the algebra of observables for an infinitely extended quantum spin system and study their relationship. In particular, we show that the ubiquitous characterization which arises from the Lieb-Robinson bound implies but is not equivalent to continuity with respect to the natural Fr\'echet topology of almost local observables, which is a non-commutative analog of the Schwartz space.
Cite
@article{arxiv.2512.02181,
title = {The Lieb-Robinson condition and the Fr\'echet topology},
author = {Sven Bachmann and Giuseppe De Nittis and Julián Gómez},
journal= {arXiv preprint arXiv:2512.02181},
year = {2025}
}
Comments
38 pages. Keywords: Spin lattice systems, almost local algebras, Fr\'echet algebras, Lieb-Robinson bounds, ALP-automorphisms