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We propose to realize an exotic Haldane superfluid (HSF) phase in an extendedBose-Hubbard model on the two-leg ladder (i.e., a two-species mixture ofinteracting bosons). The proposal is confirmed by means of large-scale quantumMonte Carlo simulations, with a significant part of the ground-state phasediagram being revealed. Most remarkably, the newly discovered HSF phasefeatures both superfluidity and the non-local topological Haldane order. Theeffects induced by varying the number of legs are furthermore explored. Ourresults shed light on how topological superfluid emerges in bosonic systems.

Exotic Haldane Superfluid Phase of Soft-Core Bosons in Optical Lattices