Some Properties of Anyons

Cao, Zhenbin, Liu Liu +3 more

良久 北沢

Bert Schroer

Yajiang Hao

Using an anyon-fermion mapping method, we investigate the ground-state properties of hard-core anyons confined in a one-dimensional harmonic trap. The concise analytical formula of the reduced one-body density matrix is obtained. Based on this formula, we evaluated the momentum distribution, the natural orbitals, and their occupation distributions for different statistical parameters. The occupation and occupation fraction of the lowest natural orbital versus anyon number are also displayed. It is shown that the ground-state properties of anyons interplay between bosons and fermions continuously. We can expect that the hard-core anyons of larger statistical parameters exhibit similar properties to the hard-core bosons although anyon systems satisfy specific fractional statistics.

Václav Zatloukal, Lauri Lehman, Sukhwinder Singh +2 more

The quasi-one-dimensional transport of Abelian and non-Abelian anyons is studied in the presence of a random topological background. In particular, we consider the quantum walk of an anyon that braids around islands of randomly filled static anyons of the same type. Two distinct behaviors are identified. We analytically demonstrate that all types of Abelian anyons localize purely due to the statistical phases induced by their random anyonic environment. In contrast, we numerically show that non-Abelian Ising anyons do not localize. This is due to their entanglement with the anyonic environment, which effectively induces dephasing. Our study demonstrates that localization properties strongly depend on nonlocal topological interactions, and it provides a clear distinction in the transport properties of Abelian and non-Abelian anyons.

Ijaz Durrani