Pfaffian-like ground state for 3-body-hard-core bosons in 1D lattices

We propose a Pfaffian-like Ansatz for the ground state of bosons subject to 3-body infinite repulsive interactions in a 1D lattice. Our Ansatz consists of the symmetrization over all possible ways of distributing the particles in two identical Tonks-Girardeau gases. We support the quality of our Ansatz with numerical calculations and propose an experimental scheme based on mixtures of bosonic atoms and molecules in 1D optical lattices in which this Pfaffian-like state could be realized. Our findings may open the way for the creation of non-abelian anyons in 1D systems.