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, finding a clear route to realize non-Abelian quantum Hall states in these systems remains challenging. Here we use the density-matrix renormalization-group (DMRG) method to study the Hofstadter-Bose-Hubbard model at filling factor v = 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 non-Abelian Pfaffian. We study the on-site correlations of the ground state, which indicate its paired nature at v = 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 current cold atom experiments and we show that the Pfaffian-like state is readily realizable in few-body systems using adiabatic preparation schemes.

Automated summary

In this study, the authors use the DMRG method to investigate the Hofstadter-Bose-Hubbard model and find that under specific conditions, its ground state is a non-Abelian Pfaffian analog with paired characteristics and a charge gap in the bulk. The behaviors of two- and three-particle correlation functions, as well as the emergence of charge density waves, serve as evidence for the close relationship between this state and the continuum Pfaffian. The discussed signatures are observable in current cold atom experiments, and the Pfaffian-like state can be readily realized in few-body systems using adiabatic preparation schemes.