Composite anyons on a torus

TL;DR

This paper constructs and analyzes wave functions for anyons on a torus, exploring their topological properties and energy gaps as the statistical flux varies, bridging quantum Hall effects and composite fermions.

Contribution

It provides explicit wave functions for anyons on a torus, including their topological invariants and energy gaps, extending previous models to a more general setting.

Findings

Energy gap remains open as statistical phase varies

Wave functions can be projected into the lowest Landau level

Topological quantities like degeneracy and Chern number are computed

Abstract

An adiabatic approach put forward by Greiter and Wilczek interpolates between the integer quantum Hall effects of electrons and composite fermions by varying the statistical flux bound to electrons continuously from zero to an even integer number of flux quanta, such that the intermediate states represent anyons in an external magnetic field with the same "effective" integer filling factor. We consider such anyons on a torus, and construct representative wave functions for their ground as well as excited states. These wave functions involve higher Landau levels in general, but can be explicitly projected into the lowest Landau level for many parameters. We calculate the variational energy gap between the first excited state and ground state and find that it remains open as the statistical phase is varied. Finally, we obtain from these wave functions, both analytically and numerically, various topological quantities, such as ground-state degeneracy, the Chern number, and the Hall viscosity.