Exact Ground State Wave Functions for N Anyons in a Magnetic Field on a Torus

TL;DR

This paper derives the exact ground state wave functions for N anyons in a magnetic field on a torus, considering filling factors up to one, using Chern-Simons theory and gauge transformations.

Contribution

It provides explicit ground state wave functions for anyons on a torus, advancing understanding of their quantum states in magnetic fields.

Findings

Derived complete ground state wave functions for N anyons.

Demonstrated the multi-component nature of wave functions after gauge transformation.

Confirmed consistency with previous studies on anyon wave functions.

Abstract

The complete set of ground state wave functions for N anyons in an external magnetic field on the torus is found. The cases when the filling factor is less than or equal to one are considered. The single valued description of anyons is employed through out by coupling bosons to a Chern-Simons field. At the end, the Chern-Simons interaction is removed by a singular gauge transformation as a result of which the wave functions become multi-component in agreement with other studies.