张量网络与神经网络在物理学中的应用和交融

基金项目: 国家自然科学基金(批准号：11774420)、国家重点研发计划(批准号：2016YFA0300503，2017YFA0302900)和中国人民大学研究基金(批准号:20XNLG19)资助项目

Tensor networks and neural networks: applications and interplays in physics

摘要: 基于张量网络的数值重正化群方法，被广泛地应用到物理学的研究中，已经成为量子多体计算方法大家庭的重要一员。近年来，基于神经网络的机器学习方法也逐渐渗透到物理学领域，并被成功应用在量子多体等问题的研究中。文章简要综述了近年来张量网络和神经网络在凝聚态物理和统计物理学的应用，并讨论了两者的相互交叉和结合。
- 张量网络 /
- 神经网络 /
- 数值重正化群 /
- 交融
Abstract: The numerical renormalization group method based on tensor networks is widely used in physics, and has become an important member in the family of quantum manybody computational methods. In recent years, machine learning based on neural networks has entered the physical community, and has been successfully applied to quantum many- body systems. This review gives a brief survey about the applications of the two networks in condensed matter physics and statistical physics, and discusses their interplay and combinations.
- tensor network /
- neural network /
- numerical renormalization group /
- interplay