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

Abstract

We analyze interacting ultracold bosonic atoms in a one-dimensional superlattice potential with alternating tunneling rates t1 and t2 and inversion symmetry, which is the bosonic analogue of the Su-Schrieffer-Heeger model. A Z2 topological order parameter is introduced which is quantized for the Mott insulating (MI) phases. Depending on the ratio t1/t2 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.

Generalized Aubry-André-Harper model withp-wave superconducting pairing

“…With the realization of the AAH model in photonic crystals [15][16][17] and ultracold atoms [18,19], this model has gained attention in recent years. The abundant phenomena revealed by the AAH model make it an ideal test field for topological phases and the transitions between them both in the incommensurate and commensurate cases [20][21][22][23][24][25][26][27][28][29][30]. When the lattice is incommensurate, the system will go through a transition from an extended phase to a localized phase due to the disordered on-site potential [23,24].…”

Anderson localization in the non-Hermitian Aubry-André-Harper model with physical gain and loss

“…It is well known that the Aubry-André model or the Aubry-André-Harper (AAH) model will shows a phase transition from extended states to localized states (Anderson localization) when the lattice is incommensurate [35][36][37][38]. The normal Hermitian AAH model with or without p-wave superconducting pairing presents abundant physical phenomena both in the commensurate and incommensurate situations [39][40][41][42][43][44][45][46][47][48][49][50][51]. However, the influences of physical gain and loss on the AAH model have not been explored much.…”

Cluster Gutzwiller study of the Bose-Hubbard ladder: Ground-state phase diagram and many-body Landau-Zener dynamics

“…However, the atoms in each double-well cluster may still freely move between the two wells and so that the total atomic numbers per cluster may be odd integer numbers. The insulator phases of fractional filling numbers have also been found in one-dimensional superlattice BH models [16,29] via mean-field method, quantum Monte Carlo simulation and numerical density matrix renormalization group simulation. Different from the one-dimensional superlattice BH chains [16,29], our ladder system includes two coupled one-dimensional BH chains and the coupling between different clusters are more complex.…”

“…For an example, the experimental realization of the one-dimensional (1D) atomic Hubbard model [12] provides new opportunities to exploring quantum statistical effects and strong correlation effects in low-dimensional quantum many-body systems [13]. Quantum dynamics as well as quantum phase transition between superfluid (SF) phase and Mott insulator (MI) phase in BH models are of great interests and have been widely investigated [14][15][16][17][18][19][20][21].…”