Quantum walks of two interacting anyons in one-dimensional optical lattices

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. 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 space show uniform behaviors from antibunching to cowalking 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.