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活动主题：量子多体物理暑期学校

活动类型：暑期学校

举办单位：物理化学科教平台

活动时间：2024-08-01至08-07

活动地点：科研一号楼1040阶梯教室

面向群体：校内外研究生以及青年教师

主讲嘉宾：

王艳成，北京航空航天大学杭州国际创新学院副教授。2013年在北京师范大学物理学取得博士学位、之后在中科院物理所从事博士后研究，2017年底加入中国矿业大学材料与物理学院，2022年6月加入北航杭州国际创新学院。主要从事量子多体系统中新奇量子相与量子相变的研究。

严正，现任西湖大学物理系特聘研究员，量子多体计算实验室PI。2013年获大连理工大学学士学位，2019年获得复旦大学理论物理博士学位。2019年开始在香港大学工作，历任博士后研究员和研究助理教授。2023年加入西湖大学，同年获得国家高层次青年人才项目资助。课题组主要开展量子多体理论和数值计算方向的研究，以及与之相关的量子模拟/计算、量子材料交叉学科研究。目前发表论文约40篇，大多数是Phys. Rev. B。

Hanqing Wu completed his Ph.D. in Physics from Renmin University of China in June 2016. Afterwards, he found a postdoctoral position at California State University, Northridge. In December 2017, he became an Associate Professor at the School of Physics, Sun Yat-sen University. His research focuses on computational quantum many-body physics, where he applies numerical methods like exact diagonalization, density-matrix renormalization group, and determinant quantum Monte Carlo to study topics including frustrated quantum magnetism, spin liquids, magnetic excitations, and interacting topological phases.

张龙2015年毕业于清华大学高等研究院，获得博士学位，2015-2017年在北京大学物理学院从事博士后研究。2017年入职中国科学院大学卡弗里理论科学研究所，现任长聘副教授。主要研究方向为关联电子体系与量子相变理论。

Shenghan Jiang is an Assistant Professor at the Kavli Institute for Theoretical Sciences, University of Chinese Academy of Sciences. He earned his Ph.D. from Boston College in 2017, and subsequently served as a Postdoctoral Researcher at Caltech until 2020. His research focuses on topological phases, quantum phase transitions, and quantum computations.

叶鹏，中山大学教授，2007年6月在中山大学物理系获理学学士学位。2012年6月在清华大学高等研究院获物理学博士学位。2012年9月-2018年8月分别任职于加拿大圆周理论物理研究所和美国伊利诺伊大学香槟分校物理系与凝聚态理论研究所从事博士后研究工作、任Gordon&Betty Moore Fellow。2018年8月受聘为中山大学物理学院教授兼博士生导师至今。

内容摘要：

《蒙特卡罗方法》：本次课程将分三个部分展开：第一部分介绍经典蒙特卡洛方法。第二部分介绍有限尺寸标度理论。最后一部分主要介绍量子多体系统中比较常用的计算方法——随机序列展开（stochastic series expansion，SSE）的量子蒙特卡罗方法。我们将以有向圈（（directed loop）算法为例，详细给出该算法的基本思路以及程序实现。进一步结合具体实例展示该算法在实际量子多体计算中的应用。

《如何通过量子蒙卡提取自旋系统中的量子纠缠信息》：本次课程将重点讲述路径积分形式的蒙卡如何在自旋和玻色系统中提取多体纠缠信息，包括：纠缠熵、纠缠谱、纠缠哈密顿量等。当然也会穿插介绍这些纠缠物理量的用途，比如探测对称性破缺、临界行为、共形场论等。

Introductions and applications of Exact diagonalization and determinant quantum Monte Carlo：In the morning session, I will start by introducing exact diagonalization, which is a crucial quantum toolbox for solving quantum many-body problems. I will then provide details on the Lanczos technique, including how it uses symmetries and sparse matrix storage formats, among other key elements. Following that, I will present some of our recent applications of this method to spin, fermion, and hard-core boson systems. If time allows, I will also introduce the fundamental ED code. In the afternoon course, I will introduce the projective formalism of determinant quantum Monte Carlo, a method for performing large-scale simulations of ground states. I will take you through the process, explaining how this method transforms quantum mechanical problems into a classical summation over auxiliary fields. Finally, I will show you some of our recent applications of this approach to various Hubbard models.

《相变和重整化》：The basic theory of phase transitions and critical phenomena will be introduced in this short-term course. The classical and quantum Ising models in various spatial dimensions will be taken as prominent examples. The following topics will be covered: 1. Classical and quantum Ising models; 2. Block transformation and renormalization group flow; 3. Fixed point, scaling and universality; 4. Exact solution of 1D quantum Ising models; 5. Cluster Ising models and topology; 6. Duality of 2D Ising model; 7. Duality of 3D Ising model; 8. Z2 gauge theory, toric code model.

Topological phases in tensor network states：Tensor network states are a powerful tool for studying correlated systems. In this series of lectures, we will focus on the tensor network representation of topological phases. Starting with a brief introduction to tensor network states, we will then delve into the classification of one-dimensional topological phases using tensor network states. We will discuss both boson and fermion systems. If time permits, we will also explore two-dimensional topological phases.

Free fermion Entanglement and Fractonic superfluids：In the first part of this course, I will introduce entanglement scaling behaviors in free fermion systems, especially focusing on the applicability of Widom conjecture, non-translationally invariant and non-Euclidean lattices. In the second part of this course, I will move to the idea of many-body systems with higher-rank symmetry, in which higher moments, e.g., dipoles, are conserved. Considering such symmetry breaking leads to exotic “fractonic superfluids”. I will introduce the basic theory of this kind of symmetry-breaking phases, including low-energy effective field theory, Goldstone bosons, Gross-Pitaevskii equations, symmetry-defects, etc.

联系人：物理化学科教平台，王艳成ycwangphys@buaa.edu.cn