Fractional Quantum Hall States in Fast Rotating Bose Gases

TL;DR

This paper models fractional quantum Hall states in fast rotating Bose gases using a Chern-Simons Landau-Ginzburg framework, predicting a rich set of filling factors and proposing a phase diagram for these states.

Contribution

It introduces a bosonic analog of the law of corresponding states and predicts a broader spectrum of fractional quantum Hall states in rotating Bose gases.

Findings

Predicted filling factors include all fractions with even product pq.

Numerically favored fractional states are identified.

A tentative phase diagram for ν<1 is proposed.

Abstract

We use a Chern Simons Landau-Ginzburg (CSLG) framework related to hierarchies of composite bosons to describe 2D harmonically trapped fast rotating Bose gases in Fractional Quantum Hall Effect (FQHE) states. The predicted values for $\nu$ (ratio of particle to vortex numbers) are $\nu$$=$${{p}\over{q}}$ ($p$, $q$ are any integers) with even product $pq$, including numerically favored values previously found and predicting a richer set of values. We show that those values can be understood from a bosonic analog of the law of the corresponding states relevant to the electronic FQHE. A tentative global phase diagram for the bosonic system for $\nu$$<$1 is also proposed.