Numerical test of bosonization of the 1/3 FQHE edge

T. Bakeyev, Alexander I. Veselov, M. I. Polikarpov +1 more

Nicolas Regnault

The system of neutral bosons in rapidly rotating atomic trap is equivalent to charged bosons coupled to a magnetic field, which has opened up the possibility of fractional quantum Hall effect (FQHE) for bosons interacting with a short range interaction. We present numerical evidences for incompressible liquids at filling fractions ν = 1/2, 2/3, 3/4. Motivated by the composite fermion (CF) theory of the FQHE for electrons, we show how interacting bosons can be mapped into non-interacting spinless fermions carrying one vortex each. This provides an elegant explanation of the fractional quantum Hall states in this system. We use overlap calculations to test how the CF model fits with exact numerical results. At ν = 1, the fermionization appears to overcompensate for the repulsive interaction between bosons producing an attractive interaction between fermions, as evidence by a pairing of fermions. In that case, the Pfaffian state is a good candidate to describe the ground state of such system.

Akiomi Mishima, 実 木村

Sudhansu S. Mandal, Jainendra K. Jain

Vladimir A. Zyuzin

Wenjun Zheng

We derive a microscopic theory of the composite particles describing the low-lying edge excitations in the fractional quantum Hall liquid with ν=1/m. Using the composite-particle transformation, one finds that the edge states of the system in a disc sample are described by the Calogero–Sutherland model with other interactions between the composite particles as perturbations. The effects of both the interactions and the confinement potential are considered, and proved unable to change the exponent g=ν=1/m. We also obtain the important chiral condition at the mean field level, and as a result justify microscopically the Chiral Luttinger Liquid model of the FQHE edge states.