Pfaffian statistics through adiabatic transport in the 1D coherent state representation

TL;DR

This paper demonstrates that charge-density-wave patterns in thin torus limits determine the non-abelian statistics of the Moore-Read state, using adiabatic continuity and topological principles in quantum Hall systems.

Contribution

It shows that simple charge-density-wave patterns in the thin torus limit encode the non-abelian statistics of the Moore-Read state, linking microscopic patterns to topological properties.

Findings

Charge-density-wave patterns determine non-abelian statistics.

Adiabatic continuity connects thin torus patterns to bulk properties.

Method relies on noncommutative geometry and topological arguments.

Abstract

Recent work has shown that the low energy sector of certain quantum Hall states is adiabatically connected to simple charge-density-wave patterns that appear, e.g., when the system is deformed into a thin torus. Here it is shown that the patterns emerging in this limit already determine the non-abelian statistics of the $\nu=1$ Moore-Read state. Aside from the knowledge of these patterns, the method only relies on the principle of adiabatic continuity, the effectively noncommutative geometry in a strong magnetic field, and topological as well as locality arguments.