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

Communications in Theoretical Physics 2024年第12期76卷 62-74页

作者： Cuicui Zheng Jiahui Xie Ming Zhang Yajiang Chen Yunbo Zhang Zhejiang Key Laboratory of Quantum State Control and Optical Field Manipulation Department of Physics Zhejiang Sci-Tech University

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 *** 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 Bloch oscillations quantum simulation quantum walk two-anyon states

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