The Lieb-Robinson condition and the Fréchet topology
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 Fréchet topology of almost local observables, which is a non-commutative analog of the Schwartz space.
Fields of Study & Subjects
Advanced Operator Algebra Research
Quantum Information and Cryptography
Advanced Topics in Algebra
Publication details
- Journal / source
- Journal of Mathematical Physics
- Volume
- 67
- Issue
- 7
- Publication date
- 1 July 2026
- Language
- EN