Trotter Product Formulae for *-Automorphisms of Quantum Lattice Systems
Abstract
We consider the dynamics $$t\mapsto \tau _t$$ t ↦ τ t of an infinite quantum lattice system that is generated by a local interaction. If the interaction decomposes into a finite number of terms that are themselves local interactions, we show that $$\tau _t$$ τ t can be efficiently approximated by a product of n automorphisms, each of them being an alternating product generated by the individual terms. For any integer m, we construct a product formula (in the spirit of Trotter) such that the approximation error scales as $$n^{-m}$$ n - m . Our bounds hold in norm, pointwise for algebra elements that are sufficiently well approximated by finite volume observables.
- Publication:
-
Annales Henri Poincaré
- Pub Date:
- December 2022
- DOI:
- 10.1007/s00023-022-01207-8
- arXiv:
- arXiv:2105.14168
- Bibcode:
- 2022AnHP...23.4463B
- Keywords:
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- Mathematical Physics;
- Quantum Physics
- E-Print:
- Published in Annales Henri Poincar\'e