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arXiv · 2105.14168

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

Sven Bachmann·Markus Lange
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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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Sven Bachmann, Markus Lange. 2021-05-29. Trotter product formulae for $*$-automorphisms of quantum lattice systems. https://doi.org/10.1007/s00023-022-01207-8

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