Short-time accuracy and intra-electron correlation for nonadiabatic quantum-classical mapping approaches
Year: 2024
Authors: Lang HF., Hauke P.
Autors Affiliation: Univ Trento, Pitaevskii BEC Ctr, CNR INO & Dipartimento Fis, Via Sommar 14, I-38123 Trento, Italy; Heidelberg Univ, Inst Phys Chem, Theoret Chem, Neuenheimer Feld 229, D-69120 Heidelberg, Germany; Trento Inst Fundamental Phys & Applicat, INFN TIFPA, Trento, Italy; Univ Tokyo, Grad Sch Engn, Dept Nucl Engn & Management, 7-3-1 Hongo,Bunkyo Ku, Tokyo 1138656, Japan.
Abstract: Nonadiabatic quantum-classical mapping approaches have significantly gained in popularity over the past several decades because they have acceptable accuracy while remaining numerically tractable even for large system sizes. In the recent few years, several novel mapping approaches have been developed that display higher accuracy than the traditional Ehrenfest method, linearized semiclassical initial value representation (LSC-IVR), and Poisson bracket mapping equation (PBME) approaches. While various benchmarks have already demonstrated the advantages and limitations of those methods, unified theoretical justifications of their short-time accuracy are still demanded. In this article, we systematically examine the intra-electron correlation, as a statistical measure of electronic phase space, which has been first formally proposed for mapping approaches in the context of the generalized discrete truncated Wigner approximation and which is a key ingredient for the improvement in short-time accuracy of such mapping approaches. We rigorously establish the connection between short-time accuracy and intra-electron correlation for various widely used models. We find that LSC-IVR, PBME, and Ehrenfest methods fail to correctly reproduce the intra-electron correlation. While some of the traceless Meyer-Miller-Stock-Thoss (MMST) approaches, partially linearized density matrix (PLDM) approach, and spin partially linearized density matrix (spin-PLDM) approach are able to sample the intra-electron correlation correctly, the spin linearized semiclassical (spin-LSC) approach, which is a specific example of the classical mapping model, and the other traceless MMST approaches sample the intra-correlation faithfully only for two-level systems. Our theoretical analysis provides insights into the short-time accuracy of semiclassical methods and presents mathematical justifications for previous numerical benchmarks.
Journal/Review: JOURNAL OF CHEMICAL PHYSICS
Volume: 161 (23) Pages from: 234108-1 to: 234108-16
More Information: We thank Oriol Vendrell for helpful discussions. We acknowledge Jian Liu and Youhao Shang for informing us about the work of Gerando Garcia et al. on the first implementation of Stratonovich phase space (W-version) to linearized semi-classical simulations of quantum optical systems (equivalent to Spin-LSC-W). We acknowledge the support by Provincia Autonoma di Trento, the ERC Starting Grant StrEnQTh (Pr oject-ID 804305), and Q@TN-Quantum Science and Technology in Trento. P.H. received funding from the Italian Ministry of University and Research (MUR) through the FARE grant for the project DAVNE (Grant No. R20PEX7Y3A). This project was funded within the QuantERA II Programme that has received funding from the European Union’s Horizon 2020 research and innovation program under Grant Agreement No. 101017733, by the European Union under NextGenerationEU, PRIN 2022 Project No. 2022ATM8FY (CUP: E53D23002240006), by the European Union under NextGenerationEU via the ICSC-Centro Nazionale di Ricerca in HPC, Big Data and Quantum Computing. Views and opinions expressed are, however, those of the author(s) only and do not necessarily reflect those of the European Union, The European Research Executive Agency, or the European Commission. Neither the European Union nor the granting authority can be held responsible for them.KeyWords: Zero-point-energy; Phase-space; Dynamics; Field; Representation; Approximation; Exploration; Simulations; Formulation; FreedomDOI: 10.1063/5.0242276