A perspective on anyonic braiding statistics

TL;DR

This paper discusses the significance and limitations of recent experimental measurements of anyonic braiding phases, highlighting that current methods only partially verify theoretical predictions for quasiparticle statistics.

Contribution

It provides a critical analysis of experimental approaches to measuring anyonic braiding statistics, emphasizing the limitations in fully confirming theoretical models.

Findings

Experimental results confirm quasiparticles are anyons.

Measured phase matches theoretical predictions.

Current methods only determine statistics parameter modulo π.

Abstract

We comment on the significance of the results in the paper by Nakamura et al (2020). The experimental result measures the phase for a repeated elementary exchange of two identical quasiparticles, and shows that the quasiparticles are anyons. The value of the phase agrees with theoretical predictions. However, in terms of the statistics parameter $\theta$ for a single elementary exchange, it determines $2\theta$ modulo $2\pi$, and hence $\theta$ only modulo $\pi$, not modulo $2\pi$, and so does not fully check the theoretical prediction for the braiding statistics of charge $e/3$ quasiparticles. This is a general shortcoming of this particular type of interference measurement of statistics.