Effect of Inter-particle Interactions on Pair Correlations of One-Dimensional Anyon Gases

Abstract

The pair correlation function of the one-dimensional interacting anyonic system in its ground state is investigated based on the exact Bethe ansatz solution for arbitrary coupling constant (\(0\le c\le \infty \)) and statistics parameter (\(0\le \kappa \le \pi \)). We discuss the effects of the inter-particle interactions and the fractional statistics on the pair correlations in both position and momentum spaces. The pair correlations of anyons with coupling constant c and statistical parameter \(\kappa \) in position space are identical to that of the Lieb–Liniger Bose model with effective coupling constant \(c^{^{\prime }}=c/\cos \left( \kappa /2\right) \). Besides the effect of renormalized coupling, the correlations in momentum space reveal more effects induced by the statistics parameter. The anyonic statistics results in the nonsymmetric correlation when the statistics parameter deviates from 0 (Bose statistics) and \(\pi \) (Fermi statistics) for any coupling constant c. The correlations display peaks and dips, representing the bunching and antibunching of atoms, respectively. The correlations show crossover from bunching behavior of bosons to antibunching behavior of fermions as \(\kappa \ \) varies from 0 to \(\pi \) for arbitrary coupling constant. Besides the fractional effect, we also observe the effects induced by the inter-particle interactions in the momentum correlations. With the increase of the coupling constant, the bunching effect between particles weakens and the antibunching points in the correlations shift.