Strongly interacting mesoscopic systems of anyons in one dimension

TL;DR

This paper provides exact solutions for small systems of anyons in one dimension, revealing how their mixing behavior depends on interactions, external confinement, and how to probe their statistical properties experimentally.

Contribution

It introduces exact solutions for few-body anyonic systems in 1D and explores their mixing properties and methods to measure their statistical parameter.

Findings

Demixing depends on external trap configuration.

Exact solutions for up to six strongly interacting anyons.

Proposed experimental methods to measure anyonic statistics.

Abstract

Using the fractional statistical properties of so-called anyonic particles, we present exact solutions for up to six strongly interacting particles in one-dimensional confinement that interpolate the usual bosonic and fermionic limits. Specifically, we consider two-component mixtures of anyons and use these to eludicate the mixing-demixing properties of both balanced and imbalanced systems. Importantly, we demonstrate that the degree of demixing depends sensitively on the external trap in which the particles are confined. We also show how one may in principle probe the statistical parameter of an anyonic system by injection a strongly interacting impurity and doing spectral or tunneling measurements.