2020/09/30 by Zhiyuan Wang, Michael Foss-Feig, Kaden R. A. Hazzard
Computer Science · Physics and Astronomy · #Boundary (topology) #Boundary value problem #Bounding overwatch #Hilbert space #Ising model #Observable #Periodic boundary conditions #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum many-body systems #Upper and lower bounds #cond-mat.stat-mech #quant-ph
paper · pdf · doi:10.1103/physrevresearch.3.l032047
published as Phys. Rev. Research 3, 032047 (2021)
openalex created_date 2020/10/01 · arxiv created 2021/05/04 · openalex publication_date 2021/08/16 · arxiv updated 2021/08/25 · openalex updated_date 2026/08/06
Finite-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 | (t ) L -(t ) | C(2vt/L) cL- , with v, C, c, 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.