Fractionalization via $\mathbb{Z}_{2}$ Gauge Fields at a Cold Atom Quantum Hall Transition

TL;DR

This paper investigates a topological quantum phase transition in a cold atom system, showing how a fermionic quantum Hall state transitions to a bosonic fractional quantum Hall state via a $ ext{Z}_2$ gauge field, with charge fractionalization as a key feature.

Contribution

It introduces a dual theory with a $ ext{Z}_2$ gauge field to describe the transition and demonstrates charge fractionalization arising from this topological phase change.

Findings

The transition belongs to the (2+1)-D Ising universality class.

Charge fractionalization occurs at the quantum phase transition.

Experimental signatures of the topological transition are proposed.

Abstract

We study a single species of fermionic atoms in an "effective" magnetic field at total filling factor $\nu_{f}=1$, interacting through a p-wave Feshbach resonance, and show that the system undergoes a quantum phase transition from a $\nu_{f} =1 $ fermionic integer quantum Hall state to $\nu_{b} =1/4 $ bosonic fractional quantum Hall state as a function of detuning. The transition is in the $(2+1)$-D Ising universality class. We formulate a dual theory in terms of quasiparticles interacting with a $\mathbb{Z}_{2}$ gauge field, and show that charge fractionalization follows from this topological quantum phase transition. Experimental consequences and possible tests of our theoretical predictions are discussed.