Quantum statistics transmutation via magnetic flux attachment

TL;DR

This paper demonstrates how strong coupling between tracer and bath particles in a 2D quantum system under a magnetic field can cause a change in quantum statistics, supported by rigorous energy calculations.

Contribution

It provides a rigorous proof of quantum statistics transmutation in a 2D magnetic system using random matrix theory techniques.

Findings

Tracers change their quantum statistics when strongly coupled to a fermionic bath.

Energy estimates confirm the occurrence of statistics transmutation.

The proof involves characteristic polynomial estimates of the Ginibre ensemble.

Abstract

We consider a model for two types (bath and tracers) of 2D quantum particles in a perpendicular magnetic field. Interactions are short range and inter-species, and we assume that the bath particles are fermions, all lying in the lowest Landau level of the magnetic field. Heuristic arguments then indicate that, if the tracers are strongly coupled to the bath, they effectively change their quantum statistics, from bosonic to fermionic or vice-versa. We rigorously compute the energy of a natural trial state, indeed exhibiting this phenomenon of statistics transmutation. The proof involves estimates for the characteristic polynomial of the Ginibre ensemble of random matrices.