Fractional Chern Insulators and the W-Infinity Algebra

TL;DR

This paper demonstrates that Chern insulators with constant Berry curvature exhibit an algebraic structure akin to the W-Infinity algebra, enabling the realization of fractional quantum Hall physics on lattice systems.

Contribution

It reveals that the algebra of projected density operators in Chern insulators closes at long wavelengths and matches the W-Infinity algebra, linking lattice models to Landau level physics.

Findings

Algebra of Chern band projected densities closes at long wavelengths.

Under constant Berry curvature, this algebra is isomorphic to the W-Infinity algebra.

Provides a framework to emulate Landau level physics in lattice systems.

Abstract

A set of recent results indicates that fractionally filled bands of Chern insulators in two dimensions support fractional quantum Hall states analogous to those found in fractionally filled Landau levels. We provide an understanding of these results by examining the algebra of Chern band projected density operators. We find that this algebra closes at long wavelengths and for constant Berry curvature, whereupon it is isomorphic to the W-Infinity algebra of lowest Landau level projected densities first identified by Girvin, MacDonald and Platzman [Phys. Rev. B 33, 2481 (1986).] For Hamiltonians projected to the Chern band this provides a route to replicating lowest Landau level physics on the lattice.