Trotter product formulae for $\ast$-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 in norm, pointwise for algebra elements that are sufficiently well approximated by finite volume observables.

Published in Annales Henri Poincaré

References in corpus (4)

• Probing many-body dynamics on a 51-atom quantum simulator
• Propagation of Correlations in Quantum Lattice Systems
• Hamiltonian simulation in the low-energy subspace
• A converse to Lieb-Robinson bounds in one dimension using index theory

Cited by in corpus (2)

• On Strong Bounds for Trotter and Zeno Product Formulas with Bosonic Applications
• Convergence Rates for the Trotter Splitting for Unbounded Operators