An explicit realization of fractional statistics in one dimension

TL;DR

This paper demonstrates a way to realize fractional statistics in one-dimensional systems using the three-body Calogero model, showing how exchange phases and quantized angular momentum emerge in this context.

Contribution

It provides an explicit construction of anyons in one dimension through the Calogero model, revealing band structure and phase behavior analogous to two-dimensional anyons.

Findings

Angular spectrum exhibits band structure for -1/4<g<0

Wave function acquires the desired exchange phase

Angular momentum is quantized similarly to 2D anyonic systems

Abstract

An explicit realization of anyons is provided, using the three-body Calogero model. The fact that in the coupling domain, $-1/4<g<0$, the angular spectrum can have a band structure, leads to the manifestation of the desired phase in the wave function, under the exchange of the paticles. Concurrently, the momentum corresponding to the angular variable is quantized, exactly akin to the relative angular momentum quantization in two dimensional anyonic system