Quantum phase diagram of the integrable px+ ipy fermionic superfluid

We determine the zero-temperature quantum phase diagram of a px+ ipy pairing model based on the exactly solvable hyperbolic Richardson-Gaudin model. We present analytical and large-scale numerical results for this model. In the continuum limit, the exact solution exhibits a third-order quantum phase transition, separating a strong-pairing from a weak-pairing phase. The mean-field solution allows to connect these results to other models with px+ ipy pairing order. We define an experimentally accessible characteristic length scale, associated with the size of the Cooper pairs, that diverges at the transition point, indicating that the phase transition is of a confinement-deconfinement type without local order parameter. We propose an experimental measurement to detect the transition. We show that this phase transition is not limited to the px+ ipy pairing model but can be found in any representation of the hyperbolic Richardson-Gaudin model and is related to a symmetry that is absent in the rational Richardson-Gaudin model.