Pfaffian-like ground states for bosonic atoms and molecules in 1D optical lattices

We study ground states of a system of bosonic atoms and diatomic Feshbach molecules trapped in a one-dimensional optical lattice using exact diagonalization and Variational Monte Carlo methods. We primarily study the case of an average filling of one boson per site. In agreement with bosonization theory, we show that the ground state of the system in the thermodynamic limit corresponds to the Pfaffian-like state when the system is tuned towards the superfluid to Mott insulator quantum phase transition. Our study clarifies possibility of the creation of exotic Pfaffian-like states in realistic one-dimensional systems. Such states could be used as the basis to create non-Abelian anyons in one-dimensional systems, with potential application for fault tolerant topological quantum computation.