Higher order decompositions of ordered operator exponentials

Nathan Wiebe*, Dominic Berry, Peter Høyer, Barry C. Sanders

*Corresponding author for this work

Research output: Contribution to journalArticle

57 Citations (Scopus)

Abstract

We present a decomposition scheme based on Lie-Trotter-Suzuki product formulae to approximate an ordered operator exponential with a product of ordinary operator exponentials. We show, using a counterexample, that Lie-Trotter-Suzuki approximations may be of a lower order than expected when applied to problems that have singularities or discontinuous derivatives of appropriate order. To address this problem, we present a set of criteria that is sufficient for the validity of these approximations, prove convergence and provide upper bounds on the approximation error. This work may shed light on why related product formulae fail to be as accurate as expected when applied to Coulomb potentials.

Original languageEnglish
Article number065203
Pages (from-to)1-20
Number of pages20
JournalJournal of Physics A: Mathematical and Theoretical
Volume43
Issue number6
DOIs
Publication statusPublished - 2010

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