Fractional Quantum Hall Effect and Featureless Mott Insulators

TL;DR

This paper reveals a direct connection between featureless Mott insulators and fractional quantum Hall liquids by mapping the Hamiltonian of interacting bosons in the lowest Landau level onto a simple lattice model using magnetic Wannier states.

Contribution

It explicitly demonstrates the mapping between fractional quantum Hall states and featureless Mott insulators using magnetic Wannier states in the lowest Landau level.

Findings

Hamiltonian of interacting bosons in LLL maps onto a featureless Mott insulator Hamiltonian.

The mapped Hamiltonian includes only short-range repulsion and ring-exchange terms.

The approach simplifies understanding of fractional quantum Hall states through lattice models.

Abstract

We point out and explicitly demonstrate a close connection that exists between featureless Mott insulators and fractional quantum Hall liquids. Using magnetic Wannier states as the single-particle basis in the lowest Landau level (LLL), we demonstrate that the Hamiltonian of interacting bosons in the LLL maps onto a Hamiltonian of a featureless Mott insulator on triangular lattice, formed by the magnetic Wannier states. The Hamiltonian is remarkably simple and consists only of short-range repulsion and ring-exchange terms.