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arXiv · 2512.02181

The Lieb-Robinson condition and the Fr\'echet topology

Sven Bachmann·Giuseppe De Nittis·Julián Gómez
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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.

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Sven Bachmann, Giuseppe De Nittis, Julián Gómez. 2025-12-01. The Lieb-Robinson condition and the Fr\'echet topology. https://arxiv.org/abs/2512.02181

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