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

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.

Published version. Some references updated

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• Decomposition of fractional quantum Hall states: New symmetries and approximations
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• Repulsive Interactions in Quantum Hall Systems as a Pairing Problem
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• Deformed Fredkin model for the $\nu =5/2$ Moore-Read state on thin cylinders
• Exclusion statistics for quantum Hall states in Tao-Thouless limit