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

We study a single species of fermionic atoms in an "effective" magnetic field at total filling factor $ν_{f}=1$, interacting through a p-wave Feshbach resonance, and show that the system undergoes a quantum phase transition from a $ν_{f} =1$ fermionic integer quantum Hall state to $ν_{b} =1/4$ 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.

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