中文版 | English
Title

基于机器学习方法对分数量子霍尔系统相变的研究

Alternative Title
RESEARCH ON THE PHASE TRANSITION OF FRACTIONAL QUANTUM HALL SYSTEM BASED ON MACHINE LEARNING METHOD
Author
Name pinyin
JIN Qin
School number
11749313
Degree
博士
Discipline
070205 凝聚态物理
Subject category of dissertation
07 理学
Supervisor
王浩
Mentor unit
量子科学与工程研究院
Publication Years
2022-05-19
Submission date
2022-09-09
University
哈尔滨工业大学
Place of Publication
哈尔滨
Abstract
分数量子霍尔效应是现代凝聚态物理领域中最重要的发现之一。作为一个完全由粒子间相互作用主导的多体关联系统,分数量子霍尔系统中不断涌现出新奇的拓扑量子态。目前,人们对于这些量子相态的理解还不透彻,主要依赖于一些特定的唯象理论或模型波函数。另一方面,机器学习作为人工智能的一个重要分支,近些年在凝聚态物理方向得到了广泛的应用。但是,这些应用大多集中在一些特殊的晶格模型系统,针对分数量子霍尔系统的研究极少。
本论文将尝试利用机器学习的不同方法,对分数量子霍尔系统中由多种效应导致的各类量子态以及它们之间的相变进行系统性的研究。主要工作包括下面三个部分:
首先,利用无监督机器学习中的主成分分析法对具有分数填充因子的多个双层分数量子霍尔系统进行了研究。结果表明,在由层间隧穿效应和层间耦合作用构造的参量空间的不同物理极限下,双层系统可以呈现出不同的量子相态。
此外,研究发现即使能谱的间隙并没有完全闭合,依然可以利用主成分分析中一些共同的特征来识别两个竞争相之间的跃迁和相边界。本文进一步提供了数值证据,证实了双层系统在大的层间隧穿极限下与单层系统相似。在强相关双层极限、解耦双层极限和强层间隧穿极限时,可以应用主成分分析的一般方法来确定相的临界边界。
其次,针对具有半填充高朗道能级的量子霍尔系统,本文分别应用机器学习中的主成分分析和神经网络方法对该系统中条形电荷密度波态对抗杂质散射的鲁棒性进行了研究。通过无监督主成分分析法,本文发现,即使存在有限强度的无序散射,条形态的主要特征仍然可以由波函数中的若干主成分共同表达。
而这些关联成分随散射强度的协同坍塌,标志着系统由长程有序态向无序态的转变。本文进一步应用主成分分析和神经网络方法确定了这一相变的临界杂质散射强度。这一研究有望为后续在现实的物理系统中实验观测条形相态提供参数依据。
最后,对于填充因子为5/2这一有着偶数分母的特殊单层分数量子霍尔系统,本文用主成分分析法研究了它在粒子-空穴对称性被破坏情况下的行为。通过引入一个模型三体势来表征粒子-空穴破缺的机制,本文发现5/2系统随三体势的强度和方向分别向具有非阿贝尔统计的两类特殊拓扑量子态进行演变。而它们的转变点对应的就是粒子-空穴对称的纯库伦作用系统。由于人们未来期望利5/2系统中的这两类特殊态来设计量子比特,本文的结果揭示出粒子-空穴破缺对它们的存在将具有关键作用。
本文利用机器学习方法获得的上述研究结果,验证了机器学习作为一种新的研究手段在分数量子霍尔系统中的适用性。更进一步而言,机器学习直接分析原始的波函数,不依赖于先期经验性的理论假设和模型,因而可以被更普遍地推广应用到一些人们还不曾理解的陌生系统。
Keywords
Language
Chinese
Training classes
联合培养
Enrollment Year
2017
Year of Degree Awarded
2022-06
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Academic Degree Assessment Sub committee
物理系
Domestic book classification number
O469
Data Source
人工提交
Document TypeThesis
Identifierhttp://kc.sustech.edu.cn/handle/2SGJ60CL/395691
DepartmentDepartment of Physics
Recommended Citation
GB/T 7714
金芹. 基于机器学习方法对分数量子霍尔系统相变的研究[D]. 哈尔滨. 哈尔滨工业大学,2022.
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