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Trotter Product Formulae for ∗-Automorphisms of Quantum Lattice Systems.
- Source :
- Annales Henri Poincaré; Dec2022, Vol. 23 Issue 12, p4463-4487, 25p
- Publication Year :
- 2022
-
Abstract
- We consider the dynamics 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 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 . Our bounds hold in norm, pointwise for algebra elements that are sufficiently well approximated by finite volume observables. [ABSTRACT FROM AUTHOR]
- Subjects :
- APPROXIMATION error
ALGEBRA
BANACH algebras
INTEGERS
AUTOMORPHISMS
Subjects
Details
- Language :
- English
- ISSN :
- 14240637
- Volume :
- 23
- Issue :
- 12
- Database :
- Complementary Index
- Journal :
- Annales Henri Poincaré
- Publication Type :
- Academic Journal
- Accession number :
- 160295108
- Full Text :
- https://doi.org/10.1007/s00023-022-01207-8