Numerical exact diagonalization of singularity in the ground state of two-dimensional hydrogen atom

doi:10.7498/aps.66.230102

	Numerical exact diagonalization of singularity in the ground state of two-dimensional hydrogen atom
	Liu Chu-Hang1 ; Qiang Bai-Qiang1 ; Ji Yu-Chen1 ; Li Wei 2
	2017-12-05
发表期刊	物理学报 (IF:0.8[JCR-2023],0.8[5-Year])
ISSN	1000-3290
卷号	66 期号:23
发表状态	已发表
DOI	10.7498/aps.66.230102
摘要	With the development of computing technology, numerical exact diagonalization method plays a vital role in modern computational condensed matter physics, especially in the research area of strongly correlated electron systems: it becomes a benchmark for other numerical computational techniques, such as quantum Monte Carlo, numerical renormalization group, density matrix renormalization group, and dynamic mean field theory. In this paper, we first numerically exactly diagonalize the three-dimensional hydrogen atom with the combination of finite-difference method, and find that the numerical wave function of ground state is in good agreement with the analytical calculations. We then turn to discuss the space dimension confinement hydrogen system, two-dimensional hydrogen atom, and notice that the numerical wave function is no longer in agreement with the analytical calculation, where the ground state wave function has a numerical singularity as radius approaches to zero. Compared with the case of the three-dimensional hydrogen atom, this issue mainly comes from the nature of space dimension confinement. To resolve such an issue of numerical singularity in two-dimensional hydrogen atom, we need to construct a new discrete and normalized Bessel function as a basis to study the ground state behavior of dimension confinement system based on the framework of Lanczos-type numerical exact diagonalization. The constructed normalized Bessel basis is orthogonal and discrete, and thus becomes suitable for practical calculation. Besides, these prominent properties of such a Bessel basis greatly reduce the complexity and difficulty in practical calculation, and thus makes computing work efficient. In addition, Lanczos-type numerical exact diagonalization method can extremely speed up the process of solving the eigenvalue equation. As a result, such a high efficient calculation of our method demonstrates the consistence between numerical and analytical ground state energy value, and the corresponding wave function with enough truncated basis number. Since this kind of numerical singularity occurs in many space dimension confinement systems, our finding for constructing a new discrete Bessel basis function may be helpful in studying the quantum systems with numerical singularity behaviors in wavefunctions in future. On the other hand, it should be pointed out that the Bessel basis is incorporated into the linear augment plane wave method in the density functional theory to study the electronic band structure of the condensed material and obtain high accurate results, especially in the theoretical prediction of topological insulators and in experimental realization as well.
关键词	two-dimensional hydrogen atom discrete Bessel basis function Lanczos-type numerical exact diagonalization
收录类别	SCI ; 北大核心 ; EI
语种	中文
资助项目	Youth Innovation Promotion Association of the Chinese Academy of Sciences[2016215]
WOS研究方向	Physics
WOS类目	Physics, Multidisciplinary
WOS记录号	WOS:000417504800002
出版者	CHINESE PHYSICAL SOC
EI入藏号	20180404673165
EI主题词	Atoms ; Condensed matter physics ; Density functional theory ; Eigenvalues and eigenfunctions ; Functions ; Ground state ; Group theory ; Hydrogen ; Mean field theory ; Monte Carlo methods ; Numerical methods ; Quantum optics ; Quantum theory ; Statistical mechanics ; Wave functions
EI分类号	Chemical Products Generally:804 ; Mathematics:921 ; Mathematical Statistics:922.2 ; Atomic and Molecular Physics:931.3 ; Quantum Theory; Quantum Mechanics:931.4
原始文献类型	Article
引用统计	正在获取...
文献类型	期刊论文
条目标识符	https://kms.shanghaitech.edu.cn/handle/2MSLDSTB/14302
专题	物质科学与技术学院物质科学与技术学院_硕士生物质科学与技术学院_本科生物质科学与技术学院_博士生
通讯作者	Li Wei
作者单位	1.ShanghaiTech Univ, Sch Phys Sci & Technol, Shanghai 201210, Peoples R China 2.Chinese Acad Sci, Shanghai Inst Microsyst & Informat Technol, State Key Lab Funct Mat Informat, Shanghai 200050, Peoples R China
第一作者单位	物质科学与技术学院
第一作者的第一单位	物质科学与技术学院
推荐引用方式 GB/T 7714	Liu Chu-Hang,Qiang Bai-Qiang,Ji Yu-Chen,et al. Numerical exact diagonalization of singularity in the ground state of two-dimensional hydrogen atom[J]. 物理学报,2017,66(23).
APA	Liu Chu-Hang,Qiang Bai-Qiang,Ji Yu-Chen,&Li Wei.(2017).Numerical exact diagonalization of singularity in the ground state of two-dimensional hydrogen atom.物理学报,66(23).
MLA	Liu Chu-Hang,et al."Numerical exact diagonalization of singularity in the ground state of two-dimensional hydrogen atom".物理学报 66.23(2017).