On the anyon description of the Laughlin hole states

TL;DR

This paper explores the algebraic representation of Laughlin quasi-holes as anyons, providing explicit mappings for one and two quasi-holes and analyzing their connection to coherent states, with brief discussion on quasi-electrons.

Contribution

It offers a detailed algebraic framework for the anyon description of Laughlin hole states, including explicit mappings and state connections.

Findings

Explicit mapping for one and two quasi-holes to anyon systems

Connection between hole-states and coherent states of fundamental algebras

Brief discussion on the quasi-electron case and open questions

Abstract

We examine the anyon representation of the Laughlin quasi-holes, in particular the one-dimensional, algebraic aspects of the representation. For the cases of one and two quasi-holes an explicit mapping to anyon systems is given, and the connection between the hole-states and coherent states of the fundamental algebras of observables is examined. The quasi-electron case is discussed more briefly, and some remaining questions are pointed out.