Domain wall type defects as anyons in phase space

Abstract

We discuss how the braiding properties of Laughlin quasi-particles in quantum Hall states can be understood within a one-dimensional formalism we proposed earlier. In this formalism the two-dimensional space of the Hall liquid is identified with the phase space of a one-dimensional lattice system, and localized Laughlin quasi-holes can be understood as coherent states of lattice solitons. The formalism makes comparatively little use of the detailed structure of Laughlin wavefunctions, and may offer ways to be generalized to non-abelian states.

published version

References in corpus (9)

• Fault-tolerant quantum computation by anyons
• Beyond paired quantum Hall states: parafermions and incompressible states in the first excited Landau level
• Incompressible Quantum Liquids and New Conservation Laws
• Laughlin State on Stretched and Squeezed Cylinders and Edge Excitations in Quantum Hall Effect
• 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
• One-Dimensional Theory of the Quantum Hall System
• Wavefunctions and counting formulas for quasiholes of clustered quantum Hall states on a sphere
• Mott Insulators Without Symmetry Breaking

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