一维晶格中全同任意子的量子动力学与关联  

Quantum dynamics and correlations of indistinguishable anyons in one-dimensional lattices

作　　者：王利[1] 贾丽芳 张云波 Wang Li;Jia Li-Fang;Zhang Yun-Bo(Institute of Theoretical Physics,State Key Laboratory of Quantum Optics and Quantum Optics Devices,Collaborative Innovation Center of Extreme Optics,Shanxi University,Taiyuan 030006,China;Department of Physics and Key Laboratory of Optical Field Manipulation of Zhejiang Province,Zhejiang Sci-Tech University,Hangzhou 310018,China)

机构地区：[1]山西大学,理论物理研究所,量子光学与光量子器件国家重点实验室,极端光学协同创新中心,太原030006 [2]浙江理工大学理学院物理系,光场操控省重点实验室,杭州310018

出　　处：《物理学报》2022年第13期61-68,共8页Acta Physica Sinica

基　　金：国家自然科学基金(批准号:11404199,12147215,12074340);山西省自然科学基金(批准号:2015021012,1331KSC)资助的课题。

摘　　要：任意子介于玻色子与费米子之间,遵从奇特的分数统计,隐含着许多有趣的物理特性.本文研究了一维晶格中相互作用全同任意子的少体量子动力学及其量子关联性质.基于严格的数值方法,分析了任意子在晶格中局域粒子密度分布的动力学演化过程.结果表明,分数统计可以明显影响任意子动力学演化过程中实空间的局域粒子密度分布,产生新的动力学结构.特别地,当存在相互作用时,分数统计粒子的局域粒子密度分布会呈现有趣的依赖于相互作用性质的不对称性.最后计算了任意子的密度密度关联,分析了粒子统计性质和相互作用对体系量子关联的调制,同时进一步证实了任意子分数统计在实空间中的动力学效应.Anyons,namely particles obeying fractional quantum statistics that interpolate between bosons and fermions,possess a lot of new and exotic physical properties related to the particle exchange statistics.In this work,we explore the few-body quantum dynamics and quantum correlations of indistinguishable anyons with on-site interactions in one-dimensional lattices within the scheme of three-body continuous-time quantum walks.By employing a time-evolving block decimation(TEBD)algorithm,we numerically calculate the dynamical evolution process of the local density distribution of anyons among the whole lattice.Numerical simulations shown in the main text mainly focus on a three-body initial state as|ψ(t=0)>=a_(-1)^(+)a_(0)^(+)a_(1)^(+)|0>particles are located on neighbouring sites at lattice centre.This choice of initial state features that the three particles influence one another most strongly,while we have also implemented numerical simulations on other choices of three-body initial states as are discussed in appendix.It is shown that the local density distribution of anyons is dramatically altered by fractional particle statistics with new dynamical structure showing up during the time evolution.For free anyons,an inner cone emerges as the statistical parameter increases,while the outer cone remains robust all along.When the on-site interaction joins in,the structure of the inner cone is further modified with new features.Specifically,for interaction of finite strength,an exotic dynamical asymmetry in real space,is clearly demonstrated during the time evolution of the local density distribution for particles within the fractional statistics regime.However,for boson limit and pseudofermion limit,the time evolution of the local density distribution keeps symmetric as the three-body initial state.And remarkably,the dynamical asymmetry is interaction-dependent manifested as the local density distribution of anyons favors opposite side of the lattice for repulsive and attractive interaction,respectively.Moreover,when t

关 键 词：全同任意子 分数统计 多粒子量子行走 动力学不对称性 

分 类 号：O413[理学—理论物理]