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Non-Hermitian quantum many-body systems are a fascinating subject to beexplored. Using the generalized density matrix renormalisation group method andcomplementary exact diagonalization, we elucidate the many-body ground statesand dynamics of a 1D interacting non-Hermitian Aubry-Andre-Harper model forbosons. We find stable ground states in the superfluid and Mott insulatingregimes under wide range of conditions in this model. We reveal a skinsuperfluid state induced by the non-Hermiticity from the nonreciprocal hopping.We investigate the topology of the Mott insulating phase and find itsindependence of the non-Hermiticity. The topological Mott insulators in thisnon-Hermitian system are characterized by four equal Chern numbers and aquantized shift of biorthogonal many-body polarizations. Furthermore, we showgeneric asymmetric expansion and correlation dynamics in the system.

Skin superfluid, topological Mott insulators, and asymmetric dynamics in interacting non-Hermitian Aubry-Andre-Harper models