精确量子多体疤痕态的几个代数框架  

Several mathematical frameworks of exact quantum many-body scars

作　　者：么志远 YAO Zhiyuan(Key Laboratory of Quantum Theory and Applications of MOE,Lanzhou Center for Theoretical Physics,Key Laboratory of Theoretical Physics of Gansu Province,Lanzhou University,Lanzhou 730000,China)

机构地区：[1]量子理论及应用基础教育部重点实验室,兰州理论物理中心,甘肃省理论物理重点实验室,兰州大学,甘肃兰州730000

出　　处：《新兴科学和技术趋势》2024年第3期244-265,共22页

基　　金：国家自然科学基金(12304288,12247101)。

摘　　要：多体系统涌现出来的统计力学规律是联系微观相互作用和宏观行为的桥梁,也是定量研究平衡态宏观物理量的基础。尽管现代遍历理论显著加深了我们对经典统计力学基础的理解,但本征态热化假说(eigenstate ther-malization hypothesis,ETH)能够在更为基础的量子层面为统计物理奠定更坚实的基础。近年来,人工量子系统方面的快速发展引发了人们对孤立量子多体系统的平衡态性质及热化动力学的大量研究。强意义下的本征态热化假说,即一般相互作用系统中的每个有限能量密度的本征态都会热化,也经受住了这些考验。然而,最近里德堡原子链的实验研究却揭示了弱违背本征态热化假说系统的存在:在该系统中ETH对一组测度为零的特殊本征态,量子多体疤痕态,失效。本文先从个人视角对量子多体疤痕态研究中建立的几个有代表性的代数框架做一简要综述,之后介绍我们最近发展的、能把之前多个代数框架统一起来的关联矩阵框架。The statistical laws of many-body systems is a bridge between microscopic interactions and macroscopic behaviors,and it is also the basis of predicting equilibrium macroscopic properties in a quantitative way.While modern ergodic theory has significantly deepened our understanding of the foundations of classical statistical mechanics,the eigenstate thermalization hypothesis(ETH)can put quantum statistical physics on a more solid foundation.In recent years,the rapid development in manipulating artificial quantum systems has spurred research in equilibrium properties as well as in the thermalization dynamics of isolated quantum systems.The strong ETH,which posits that in a generic interacting many-body system,the eigenstate of every finite energy density thermalizes,has withstood these tests.However,a recent experimental study in a Rydberg atom chain has revealed the existence of a weak ergodicity-breaking system,where ETH fails in a measure-zero set of special eigenstates-quantum many-body scars(QMBS).This article gives a brief review of several paradigmatic mathematical formalisms of QMBS.It then introduces the correlation matrix framework of QMBS that unifies many previous mathematical formalisms.

关 键 词：本征态热化假说 量子多体疤痕态 对称和准对称 η-配对 关联矩阵 

分 类 号：O413[理学—理论物理]