Trotter Product Formulae for [Formula: see text] -Automorphisms of Quantum Lattice Systems

We consider the dynamics [Formula: see text] 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 [Formula: see text] can be efficiently approximated by a produ...

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Detalles Bibliográficos
Autores principales: Bachmann, Sven, Lange, Markus
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2022
Materias:
Original Paper
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9674773/
https://www.ncbi.nlm.nih.gov/pubmed/36415329
http://dx.doi.org/10.1007/s00023-022-01207-8
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author Bachmann, Sven
Lange, Markus
author_facet Bachmann, Sven
Lange, Markus
author_sort Bachmann, Sven
collection PubMed
description We consider the dynamics [Formula: see text] 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 [Formula: see text] 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 [Formula: see text] . Our bounds hold in norm, pointwise for algebra elements that are sufficiently well approximated by finite volume observables.
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spelling pubmed-96747732022-11-20 Trotter Product Formulae for [Formula: see text] -Automorphisms of Quantum Lattice Systems Bachmann, Sven Lange, Markus Ann Henri Poincare Original Paper We consider the dynamics [Formula: see text] 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 [Formula: see text] 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 [Formula: see text] . Our bounds hold in norm, pointwise for algebra elements that are sufficiently well approximated by finite volume observables. Springer International Publishing 2022-07-08 2022 /pmc/articles/PMC9674773/ /pubmed/36415329 http://dx.doi.org/10.1007/s00023-022-01207-8 Text en © The Author(s) 2022 https://creativecommons.org/licenses/by/4.0/Open AccessThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) .
spellingShingle Original Paper
Bachmann, Sven
Lange, Markus
Trotter Product Formulae for [Formula: see text] -Automorphisms of Quantum Lattice Systems
title Trotter Product Formulae for [Formula: see text] -Automorphisms of Quantum Lattice Systems
title_full Trotter Product Formulae for [Formula: see text] -Automorphisms of Quantum Lattice Systems
title_fullStr Trotter Product Formulae for [Formula: see text] -Automorphisms of Quantum Lattice Systems
title_full_unstemmed Trotter Product Formulae for [Formula: see text] -Automorphisms of Quantum Lattice Systems
title_short Trotter Product Formulae for [Formula: see text] -Automorphisms of Quantum Lattice Systems
title_sort trotter product formulae for [formula: see text] -automorphisms of quantum lattice systems
topic Original Paper
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9674773/
https://www.ncbi.nlm.nih.gov/pubmed/36415329
http://dx.doi.org/10.1007/s00023-022-01207-8
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