有限温度量子多体系统与热态张量网络

发布时间：2018-10-12 13:16

【摘要】：量子多体系统热力学性质的精确模拟在理论和实验方面都具有重要的价值。局域相互作用量子多体系统的热态满足互信息(mutual information)面积律,对于这样的系统,热态张量网络可以提供满足面积律的精确"波函数"拟设,提供了模拟有限温度系统的有力手段。文章介绍了关联格点模型在有限温度下的热态张量网络刻画及相关模拟方法。作者按照世界线热态张量网络和级数展开热态张量网络来分别介绍,并讨论了自由能极小变分原理与重正化群剪裁的优化原则。世界线框架内,人们发展了转移矩阵重正化群,基于纯化策略的有限温度密度矩阵重正化群,以及张量网络的线性重正化群等方法。在此基础上,介绍作者新近提出的级数展开热态张量网络方法,该方法受随机级数展开量子蒙特卡罗方法的启发,突破了世界线方法的局限,提高了有限温度计算重正化群模拟的精度标准,并且在计算阻挫量子自旋链模型时不会有负符号问题。此外,文章讨论了在两维格点系统上推广有限温度张量网络计算的进展和未来展望。
[Abstract]:Accurate simulation of thermodynamic properties of quantum multibody systems is of great value in both theory and experiment. The thermal state of the local interacting quantum multi-body system satisfies the mutual information (mutual information) area law. For such a system, the hot Zhang Liang network can provide an accurate "wave function" to satisfy the area law and provide a powerful means to simulate the finite temperature system. This paper introduces the description of the hot Zhang Liang network and the related simulation method of the correlation lattice model at finite temperature. In this paper, the author introduces the hot state Zhang Liang network according to the world line hot Zhang Liang network and the series expansion, and discusses the principle of minimal variation of free energy and the optimization principle of renormalization group tailoring. Within the framework of the world line, transfer matrix renormalization group, finite temperature density matrix renormalization group based on purification strategy and linear renormalization group based on Zhang Liang network have been developed. On this basis, a series expansion hot Zhang Liang network method proposed by the author is introduced. The method is inspired by the random series expansion quantum Monte Carlo method and breaks through the limitation of the world line method. The precision standard of renormalization group simulation for finite temperature calculation is improved, and there is no negative sign problem in calculating the retarded quantum spin chain model. In addition, this paper discusses the progress and future prospects of extending the finite temperature Zhang Liang network on a two dimensional lattice system.
【作者单位】：北京航空航天大学物理系;北京航空航天大学国际交叉科学研究院;
【基金】：国家自然科学基金(批准号:11504014) 北京航空航天大学卓越百人计划和拔尖人才支持计划资助项目
【分类号】：O413.3

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