Non-Hermitian quasicrystal constitutes a unique class of disordered open
system with PT-symmetry breaking, localization and topological triple phase
transitions. In this work, we uncover the effect of quantum correlation on
phase transitions and entanglement dynamics in non-Hermitian quasicrystals.
Focusing on two interacting bosons in a Bose-Hubbard lattice with
quasiperiodically modulated gain and loss, we find that the onsite interaction
between bosons could drag the PT and localization transition thresholds towards
weaker disorder regions compared with the noninteracting case. Moreover, the
interaction facilitates the expansion of the critical point of a triple phase
transition in the noninteracting system into a critical phase with mobility
edges, whose domain could be flexibly controlled by tuning the interaction
strength. Systematic analyses of the spectrum, inverse participation ratio,
topological winding number, wavepacket dynamics and entanglement entropy lead
to consistent predictions about the correlation-driven phases and transitions
in our system. Our findings pave the way for further studies of the interplay
between disorder and interaction in non-Hermitian quantum matter.Comment: 18 pages, 13 figures, revised versio