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

References in corpus (7)

• Non-Abelian Anyons and Topological Quantum Computation
• Abelian and Non-abelian Hall Liquids and Charge Density Wave: Quantum Number Fractionalization in One and Two Dimensions
• The Pfaffian quantum Hall state made simple--multiple vacua and domain walls on a thin torus
• A classification of symmetric polynomials of infinite variables -- a construction of Abelian and non-Abelian quantum Hall states
• Topological degeneracy of non-Abelian states for dummies
• Halperin (m, m',n) bilayer quantum Hall states on thin cylinders
• Domain wall type defects as anyons in phase space

Cited by in corpus (1)

• Spin chain description of rotating bosons at $\nu =1$