Quantum phase diagram of the integrable p_x+ip_y fermionic superfluid

TL;DR

This paper analyzes the quantum phase diagram of a p_x+ip_y fermionic superfluid using an exactly solvable model, revealing a third-order phase transition characterized by a diverging length scale and connecting to broader classes of models.

Contribution

It provides an exact solution and numerical analysis of the p_x+ip_y pairing model, identifying a novel third-order quantum phase transition with experimental implications.

Findings

Identifies a third-order quantum phase transition in the model.

Defines a characteristic length scale diverging at the transition.

Connects the transition to a symmetry in hyperbolic Richardson-Gaudin models.

Abstract

We determine the zero temperature quantum phase diagram of a p_x+ip_y 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 p_x+ip_y 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 show that this phase transition is not limited to the p_x+ip_y 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.