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Non-Hermitian quasicrystal constitutes a unique class of disordered opensystem with PT-symmetry breaking, localization and topological triple phasetransitions. In this work, we uncover the effect of quantum correlation onphase transitions and entanglement dynamics in non-Hermitian quasicrystals.Focusing on two interacting bosons in a Bose-Hubbard lattice withquasiperiodically modulated gain and loss, we find that the onsite interactionbetween bosons could drag the PT and localization transition thresholds towardsweaker disorder regions compared with the noninteracting case. Moreover, theinteraction facilitates the expansion of the critical point of a triple phasetransition in the noninteracting system into a critical phase with mobilityedges, whose domain could be flexibly controlled by tuning the interactionstrength. Systematic analyses of the spectrum, inverse participation ratio,topological winding number, wavepacket dynamics and entanglement entropy leadto consistent predictions about the correlation-driven phases and transitionsin our system. Our findings pave the way for further studies of the interplaybetween disorder and interaction in non-Hermitian quantum matter.

Correlation-induced phase transitions and mobility edges in an interacting non-Hermitian quasicrystal