Strongly correlated phases in rapidly rotating Bose gases

TL;DR

This paper rigorously demonstrates that rapidly rotating Bose gases with weak interactions can be effectively described by a Hamiltonian modeling the bosonic Fractional Quantum Hall Effect, with convergence towards the Laughlin wavefunction.

Contribution

First rigorous proof connecting the ground state of rotating Bose gases to the effective FQHE Hamiltonian and Laughlin states.

Findings

Ground state energy converges to the effective Hamiltonian's energy.

States converge to the bosonic Laughlin wavefunction in certain regimes.

Provides the first rigorous justification of the FQHE Hamiltonian for Bose gases.

Abstract

We consider a system of trapped spinless bosons interacting with a repulsive potential and subject to rotation. In the limit of rapid rotation and small scattering length, we rigorously show that the ground state energy converges to that of a simplified model Hamiltonian with contact interaction projected onto the Lowest Landau Level. This effective Hamiltonian models the bosonic analogue of the Fractional Quantum Hall Effect (FQHE). For a fixed number of particles, we also prove convergence of states; in particular, in a certain regime we show convergence towards the bosonic Laughlin wavefunction. This is the first rigorous justification of the effective FQHE Hamiltonian for rapidly rotating Bose gases. We review previous results on this effective Hamiltonian and outline open problems.