Trotter product formulae for $*$automorphisms of quantum lattice systems
Abstract
We consider the dynamics $t\mapsto\tau_t$ 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 $\tau_t$ 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 pointwise for algebra elements that are sufficiently well approximated by finite volume observables.
 Publication:

arXiv eprints
 Pub Date:
 May 2021
 arXiv:
 arXiv:2105.14168
 Bibcode:
 2021arXiv210514168B
 Keywords:

 Mathematical Physics;
 Quantum Physics
 EPrint:
 21 pages, 2 figures