Topological vacuum bubble by anyon braiding

TL;DR

This paper reveals that vacuum bubbles of Abelian anyons influence physical observables, challenging the traditional linked cluster theorem, and proposes their experimental detection via interference patterns in fractional quantum Hall systems.

Contribution

It demonstrates that vacuum bubbles of Abelian anyons affect physical observables, revising the conventional understanding for particles with fractional statistics.

Findings

Vacuum bubbles of Abelian anyons influence interference patterns.

Temperature-dependent phase shifts observed in fractional quantum Hall experiments.

Provides a method for direct detection of fractional anyonic statistics.

Abstract

According to a basic rule of fermionic and bosonic many-body physics, known as the linked cluster theorem, physical observables are not affected by vacuum bubbles, which represent virtual particles created from vacuum and self-annihilating without interacting with real particles. Here, we show that this conventional knowledge must be revised for anyons, quasiparticles that obey fractional exchange statistics intermediate between fermions and bosons. We find that a certain class of vacuum bubbles of Abelian anyons does affect physical observables. They represent virtually excited anyons which wind around real anyonic excitations. These topological bubbles result in a temperature-dependent phase shift of Fabry-Perot interference patterns in the fractional quantum Hall regime accessible in current experiments, thus providing a tool for direct and unambiguous observation of elusive fractional statistics.