Bosonic Pfaffian state in the Hofstadter-Bose-Hubbard model

Topological states of matter, such as fractional quantum Hall states, are an active field of research due to their exotic excitations. In particular, ultracold atoms in optical lattices provide a highly controllable and adaptable platform to study such new types of quantum matter. However, the effect of a coarse lattice on the topological states often remains poorly understood. Here we use the density-matrix renormalization-group (DMRG) method to study the Hofstadter-Bose-Hubbard model at filling factor $\nu = 1$ and find strong indications that at $\alpha=1/6$ magnetic flux quanta per plaquette the ground state is a lattice analog of the continuum Pfaffian. We study the on-site correlations of the ground state, which indicate its paired nature at $\nu = 1$, and find an incompressible state characterized by a charge gap in the bulk. We argue that the emergence of a charge density wave on thin cylinders and the behavior of the two- and three-particle correlation functions at short distances provide evidence for the state being closely related to the continuum Pfaffian. The signatures discussed in this letter are accessible in cold atom experiments and the Pfaffian-like state seems readily realizable in few-body systems using adiabatic preparation schemes.