Bounding the finite-size error of quantum many-body dynamics simulations

Simple item page
dc.citation.articleNumberL032047en_US
dc.citation.issueNumber3en_US
dc.citation.journalTitlePhysical Review Researchen_US
dc.citation.volumeNumber3en_US
dc.contributor.authorWang, Zhiyuanen_US
dc.contributor.authorFoss-Feig, Michaelen_US
dc.contributor.authorHazzard, Kaden R.A.en_US
dc.contributor.orgRice Center for Quantum Materialsen_US
dc.date.accessioned2021-10-06T14:16:27Zen_US
dc.date.available2021-10-06T14:16:27Zen_US
dc.date.issued2021en_US
dc.description.abstractFinite-size errors (FSEs), the discrepancies between an observable in a finite system and in the thermodynamic limit, are ubiquitous in numerical simulations of quantum many-body systems. Although a rough estimate of these errors can be obtained from a sequence of finite-size results, a strict, quantitative bound on the magnitude of FSE is still missing. Here we derive rigorous upper bounds on the FSE of local observables in real-time quantum dynamics simulations initialized from a product state. In d-dimensional locally interacting systems with a finite local Hilbert space, our bound implies ∣∣⟨ˆS(t)⟩L−⟨ˆS(t)⟩∞|≤C(2vt/L)cL−μ, with v, C, c, μ constants independent of L and t, which we compute explicitly. For periodic boundary conditions (PBCs), the constant c is twice as large as that for open boundary conditions (OBCs), suggesting that PBCs have smaller FSEs than OBCs at early times. The bound can be generalized to a large class of correlated initial states as well. As a byproduct, we prove that the FSE of local observables in ground-state simulations decays exponentially with L under a suitable spectral gap condition. Our bounds are practically useful in determining the validity of finite-size results, as we demonstrate in simulations of the one-dimensional (1D) quantum Ising and Fermi-Hubbard models.en_US
dc.identifier.citationWang, Zhiyuan, Foss-Feig, Michael and Hazzard, Kaden R.A.. "Bounding the finite-size error of quantum many-body dynamics simulations." <i>Physical Review Research,</i> 3, no. 3 (2021) American Physical Society: https://doi.org/10.1103/PhysRevResearch.3.L032047.en_US
dc.identifier.digitalPhysRevResearch-3-L032047en_US
dc.identifier.doihttps://doi.org/10.1103/PhysRevResearch.3.L032047en_US
dc.identifier.urihttps://hdl.handle.net/1911/111497en_US
dc.language.isoengen_US
dc.publisherAmerican Physical Societyen_US
dc.rightsPublished by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.en_US
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/en_US
dc.titleBounding the finite-size error of quantum many-body dynamics simulationsen_US
dc.typeJournal articleen_US
dc.type.dcmiTexten_US
dc.type.publicationpublisher versionen_US
Files
Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
PhysRevResearch-3-L032047.pdf
Size:
437.38 KB
Format:
Adobe Portable Document Format
Download
Collections
Faculty Publications
Physics and Astronomy Publications