{"title":"Time-dependent density matrix renormalization group method for quantum dynamics in complex systems","authors":"Jiajun Ren, Weitang Li, Tong Jiang, Yuanheng Wang, Zhigang Shuai","doi":"10.1002/wcms.1614","DOIUrl":null,"url":null,"abstract":"<p>The simulations of spectroscopy and quantum dynamics are of vital importance to the understanding of the electronic processes in complex systems, including the radiative/radiationless electronic relaxation relevant for optical emission, charge/energy transfer in molecular aggregates related to carrier mobility in organic materials, as well as photovoltaic and thermoelectric conversion, light-harvesting and spin transport, and so forth. In recent years, time-dependent density matrix renormalization group (TD-DMRG) has emerged as a general, numerically accurate and efficient method for high-dimensional full-quantum dynamics. This review will cover the fundamental algorithms of TD-DMRG in the modern framework of matrix product states (MPS) and matrix product operators (MPO), including the basic algebra with respect to MPS and MPO, the novel time evolution schemes to propagate MPS, and the automated MPO construction algorithm to encode generic Hamiltonian. Most importantly, the proposed method can handle the mixed state density matrix at finite temperature, enabling quantum statistical description for molecular aggregates. We demonstrate the performance of TD-DMRG by benchmarking with the current state-of-the-art methods for simulating quantum dynamics of the spin-boson model and the Frenkel–Holstein(–Peierls) model. As applications of TD-DMRG to real-world problems, we present theoretical investigations of carrier mobility and spectral function of rubrene crystal, and the radiationless decay rate of azulene with an anharmonic potential energy surface.</p><p>This article is categorized under:\n </p>","PeriodicalId":236,"journal":{"name":"Wiley Interdisciplinary Reviews: Computational Molecular Science","volume":null,"pages":null},"PeriodicalIF":16.8000,"publicationDate":"2022-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"20","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Wiley Interdisciplinary Reviews: Computational Molecular Science","FirstCategoryId":"92","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/wcms.1614","RegionNum":2,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 20
Abstract
The simulations of spectroscopy and quantum dynamics are of vital importance to the understanding of the electronic processes in complex systems, including the radiative/radiationless electronic relaxation relevant for optical emission, charge/energy transfer in molecular aggregates related to carrier mobility in organic materials, as well as photovoltaic and thermoelectric conversion, light-harvesting and spin transport, and so forth. In recent years, time-dependent density matrix renormalization group (TD-DMRG) has emerged as a general, numerically accurate and efficient method for high-dimensional full-quantum dynamics. This review will cover the fundamental algorithms of TD-DMRG in the modern framework of matrix product states (MPS) and matrix product operators (MPO), including the basic algebra with respect to MPS and MPO, the novel time evolution schemes to propagate MPS, and the automated MPO construction algorithm to encode generic Hamiltonian. Most importantly, the proposed method can handle the mixed state density matrix at finite temperature, enabling quantum statistical description for molecular aggregates. We demonstrate the performance of TD-DMRG by benchmarking with the current state-of-the-art methods for simulating quantum dynamics of the spin-boson model and the Frenkel–Holstein(–Peierls) model. As applications of TD-DMRG to real-world problems, we present theoretical investigations of carrier mobility and spectral function of rubrene crystal, and the radiationless decay rate of azulene with an anharmonic potential energy surface.
期刊介绍:
Computational molecular sciences harness the power of rigorous chemical and physical theories, employing computer-based modeling, specialized hardware, software development, algorithm design, and database management to explore and illuminate every facet of molecular sciences. These interdisciplinary approaches form a bridge between chemistry, biology, and materials sciences, establishing connections with adjacent application-driven fields in both chemistry and biology. WIREs Computational Molecular Science stands as a platform to comprehensively review and spotlight research from these dynamic and interconnected fields.