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Trotter Product Formulae for -Automorphisms of Quantum Lattice Systems
1Department of Mathematics, University of British Columbia, Vancouver, BC V6T 1Z2 Canada.
Abstract:
We consider the dynamics 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 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 . Our bounds hold in norm, pointwise for algebra elements that are sufficiently well approximated by finite volume observables.
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