Wang, ZhiyuanFoss-Feig, MichaelHazzard, Kaden R.A.2021-10-062021-10-062021Wang, 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.https://hdl.handle.net/1911/111497Finite-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.engPublished 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.Journal articlePhysRevResearch-3-L032047https://doi.org/10.1103/PhysRevResearch.3.L032047