高等学校化学学报 ›› 2020, Vol. 41 ›› Issue (12): 2610-2628.doi: 10.7503/cjcu20200767

• 庆祝《高等学校化学学报》复刊40周年专栏 • 上一篇    下一篇

频域空间密度矩阵重正化群的研究进展

姜童, 任佳骏, 帅志刚()   

  1. 清华大学化学系, 教育部有机光电子与分子工程重点实验室, 北京 100084
  • 收稿日期:2020-10-22 出版日期:2020-12-10 发布日期:2020-12-09
  • 通讯作者: 帅志刚 E-mail:zgshuai@tsinghua.edu.cn
  • 基金资助:
    国家自然科学基金(21788102);国家重点研发计划项目(2017YFA0204501)

Frequency Domain Density Matrix Renormalization Group

JIANG Tong, REN Jiajun, SHUAI Zhigang()   

  1. Key Laboratory of Organic OptoElectronics and Molecular Engineering,Ministry of Education,Department of Chemistry,Tsinghua University,Beijing 100084,China
  • Received:2020-10-22 Online:2020-12-10 Published:2020-12-09
  • Contact: SHUAI Zhigang E-mail:zgshuai@tsinghua.edu.cn
  • Supported by:
    ? Supported by the National Natural Science Foundation of China(21788102);the National Key Research and Development Program of China(2017YFA0204501)

摘要:

密度矩阵重正化群(DMRG)作为低维强关联体系中电子结构计算的强有力方法被广泛熟知, 并被迅速地应用于量子化学, 不仅在电子结构计算中发挥重要作用, 同时也在近几年迅速地成为复杂体系量子动力学计算的重要方法. 在DMRG框架中, 衍生出了一系列计算动态响应性质的有效方法, 并得到了广泛应用. 本文简述了DMRG的基本理论, 其矩阵乘积态(MPS)表示有效地扩展了该方法的应用范围. 重点介绍了基于线性响应理论的动态DMRG, 在频率空间求解系统在零温以及有限温度下响应性质的算法, 并介绍其在电子关联问题和电子-声子关联问题中的应用, 最后展望了该领域的未来发展方向.

关键词: 密度矩阵重正化群, 矩阵乘积态, 线性响应性质, 分子聚集体, 电子-声子耦合

Abstract:

Density matrix renormalization group(DMRG) has been developed for electron correlation in low-dimensional system and has been quickly applied to quantum chemistry as a powerful method for electronic structure calculation and for quantum dynamics of complex system. After more than 20 years of development, a series of effective methods for calculating dynamic response properties within DMRG have been developed and have been extensively applied for spectroscopy. We will first briefly describe the main features of DMRG, including its matrix product state(MPS) formulation. Based on the linear response theory, we focus on descri-bing the DMRG algorithms in frequency domain to solve the response properties both for zero temperature and finite temperature. We then introduce several most relevant applications in electronic correlation problems and electron-phonon correlation problems.

Key words: Density matrix renormalization group(DMRG), Matrix product state, Linear response property, Molecular aggregate, Electron-phonon coupling(Ed.: Y, K, S)

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