Quantum Walks of Two Interacting Anyons in 1D Optical Lattices

TL;DR

This paper explores the quantum walks of two interacting anyons in 1D optical lattices, revealing how fractional statistics influence correlation symmetries and the transition from fermionic to bosonic behaviors.

Contribution

It introduces a detailed analysis of two-anyon quantum walks considering interactions and fractional statistics, highlighting correlation asymmetries and the fermion-boson crossover.

Findings

Position correlations are symmetric in Bose and Fermi limits.

Momentum correlations show asymmetry due to fractional statistics.

Strong interactions lead to a smooth fermion-to-boson transition.

Abstract

We investigate continuous-time quantum walks of two indistinguishable anyons in one-dimensional lattices with both on-site and nearest-neighbor interactions based on the fractional Jordan-Wigner transformation. It is shown that the two-body correlations in position space are symmetric about the initial sites of two quantum walkers in the Bose limit ($\chi=0$ ) and Fermi limit ( $\chi=1$), while in momentum space this happens only in the Bose limit. An interesting asymmetry arises in the correlation for most cases with the statistical parameter $\chi$ varying in between. It turns out that the origin of this asymmetry comes from the fractional statistics that anyons obey. On the other hand, the two-body correlations of hard-core anyons in position spaceshow uniform behaviors from anti-bunching to co-walking regardless of the statistical parameter. The momentum correlations in the case of strong interaction undergo a smooth process of two stripes smoothly merging into a single one, i.e. the evolution of fermions into hard-core bosons.