Localization transitions of correlated particles in nonreciprocal quasicrystals

The interplay among interaction, non-Hermiticity, and disorder opens a new avenue for engineering novel phase transitions. We study here the spectral and localization features of two interacting bosons in one-dimensional nonreciprocal quasicrystals. Specifically, by considering a quasiperiodic Hubbard lattice with nonreciprocal hoppings, we show that the interaction can lead to a mobility edge, which arises from the fact that the bound states display a much lower threshold for spectral and extended-localized transitions than scattering states. The localization transition of bound or scattering states is accompanied by a complex-real spectrum transition. Moreover, while the two-particle localized states are robust to the boundary conditions, the two-particle extended states turn into skin modes under open boundary conditions. We also show the correlated dynamics to characterize these localization transitions. Finally, we reveal that the bound states can form a mobility edge on their own by introducing a dimerized nonreciprocal quasicrystal. Our paper may pave the way for the study of non-Hermitian few-body physics.