Related papers: Trotter product formulae for $*$-automorphisms of quantum lattice systems

Trotter product formulae for $*$-automorphisms of quantum lattice systems

URL: http://arxiv.org/abs/2105.14168v4
Date: Mon, 11 Jul 2022 16:51:10 GMT
Title: Trotter product formulae for $*$-automorphisms of quantum lattice systems
Authors: Sven Bachmann and Markus Lange
Abstract summary: We show that $tau_t$ can be efficiently approximated by a product of $n$ automorphisms. Our bounds hold in norm, pointwise for algebra elements that are sufficiently well approximated by finite volume observables.
Score: 0.0
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
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 in norm, pointwise for algebra elements that are sufficiently well approximated by finite volume observables.

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