Necessity of orthogonal basis vectors for the two-anyon problem in a one-dimensional lattice  

作　　者：Cuicui Zheng Jiahui Xie Ming Zhang Yajiang Chen Yunbo Zhang 

机构地区：[1]Zhejiang Key Laboratory of Quantum State Control and Optical Field Manipulation,Department of Physics,Zhejiang Sci-Tech University,Hangzhou 310018,China

出　　处：《Communications in Theoretical Physics》2024年第12期60-72,共13页理论物理通讯(英文版)

基　　金：Supported by National Science Foundation of China(Grant Nos.12074340 and 12474492);the Science Foundation of Zhejiang Sci-Tech University(Grants No.20062098-Y,19062463-Y and 22062344-Y)。

摘　　要：Few-body physics for anyons has been intensively studied within the anyon-Hubbard model,including the quantum walk and Bloch oscillations of two-anyon states.Recently,theoretical and experimental simulations of two-anyon states in a one-dimensional lattice have been carried out by expanding the wavefunction in terms of non-orthogonal basis vectors,resulting in nonphysical degrees of freedom.In the present work,we deduce finite difference equations for the two-anyon state in a one-dimensional lattice by solving the Schr?dinger equation with orthogonal and complete basis vectors.Such an orthogonal scheme gives all the orthogonal physical eigenstates,while the conventional(non-orthogonal)method produces many nonphysical redundant eigensolutions whose components violate the anyonic commutation relations.The dynamical property of the two-anyon states in a sufficiently large lattice is investigated and compared in both the orthogonal and conventional schemes.For initial states with two anyons at the same site or two(next-)neighboring sites,we observe the same dynamical behavior in both schemes,including the revival probability,probability density function and two-body correlation.For other initial states,the conventional scheme produces erroneous states that no longer obey the anyonic relations.The period of Bloch oscillations in the pseudo-fermionic limit has been found to be twice that in the bosonic limit,while these oscillations disappear at other statistical parameters.Our findings are vital for quantum simulations of few-body anyonic physics in lattice models.

关 键 词：anyon-Hubbard model quantum walk Bloch oscillations two-anyon states quantum simulation 

分 类 号：O413[理学—理论物理]