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Bounding the finite-size error of quantum many-body dynamics simulations
- Source :
- Physical Review Research, Vol 3, Iss 3, p L032047 (2021)
- Publication Year :
- 2021
- Publisher :
- American Physical Society, 2021.
-
Abstract
- 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 |〈S[over ̂](t)〉_{L}−〈S[over ̂](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.
Details
- Language :
- English
- ISSN :
- 26431564
- Volume :
- 3
- Issue :
- 3
- Database :
- Directory of Open Access Journals
- Journal :
- Physical Review Research
- Publication Type :
- Academic Journal
- Accession number :
- edsdoj.81553e5e94084844a2b4c1e5c2575d9a
- Document Type :
- article
- Full Text :
- https://doi.org/10.1103/PhysRevResearch.3.L032047