Topological Edge States in the One-Dimensional Superlattice Bose-Hubbard Model

We analyze interacting ultracold bosonic atoms in a one-dimensional superlattice potential with alternating tunneling rates t(1) and t(2) and inversion symmetry, which is the bosonic analogue of the Su-Schrieffer-Heeger model. A Z(2) topological order parameter is introduced which is quantized for the Mott insulating (MI) phases. Depending on the ratio t(1)/t(2) the n = 1/2 MI phase is topologically nontrivial, which results in many-body edge states at open boundaries. In contrast to the Su-Schrieffer-Heeger model the bosonic counterpart lacks chiral symmetry and the edge states are no longer midgap. This leads to a generalization of the bulk-edge correspondence, which we discuss in detail. The edge states can be observed in cold atom experiments by creating a step in the effective confining potential, e. g., by a second heavy atom species, which leads to an interface between two MI regions with filling n = 1 and n = 1/2. The shape and energy of the edge states as well as the conditions for their occupation are determined analytically in the strong coupling limit and in general by density-matrix renormalization group simulations.