Phase transitions and bunching of correlated particles in a non-Hermitian quasicrystal

Noninteracting particles in non-Hermitian quasicrystals display localization-delocalization and spectral phase transitions in complex energy plane that can be characterized by point-gap topology. Here we investigate the spectral and dynamical features of two interacting particles in a non-Hermitian quasicrystal, described by an effective Hubbard model in an incommensurate sinusoidal potential with a complex phase, and unravel some intriguing effects without any Hermitian counterpart. Owing to the effective decrease of correlated hopping introduced by particle interaction, doublon states, i.e., bound particle states, display a much lower threshold for spectral and localization-delocalization transitions than single-particle states, leading to the emergence of mobility edges. Remarkably, since doublons display longer lifetimes, two particles initially placed in distant sites tend to bunch and stick together, forming a doublon state in the long time limit of evolution, a phenomenon that can be dubbed non-Hermitian particle bunching.