# Integrable model of a $p$-wave bosonic superfluid

## TL;DR

This paper introduces an exactly solvable $p$-wave pairing model for two bosonic species, revealing a quantum phase transition between a gapless singlet pair condensate and a pair Bose superfluid, with unique critical state properties.

## Contribution

It presents a novel exactly solvable bosonic $p$-wave pairing model that shares features with fermionic models but exhibits distinct phase transition characteristics.

## Key findings

- Identifies a third order quantum phase transition in the model.
- Describes the critical state as a pair condensate similar to Moore-Read state.
- Shows the transition separates a gapless condensate from a superfluid.

## Abstract

We present an exactly-solvable $p$-wave pairing model for two bosonic species. The model is solvable in any spatial dimension and shares some commonalities with the $p + ip$ Richardson-Gaudin fermionic model, such as a third order quantum phase transition. However, contrary to the fermionic case, in the bosonic model the transition separates a gapless fragmented singlet pair condensate from a pair Bose superfluid, and the exact eigenstate at the quantum critical point is a pair condensate analogous to the fermionic Moore-Read state.