  Non-Hermitian systems have attracted considerable interest in recent years
owing to their unique topological properties that are absent in Hermitian
systems. While such properties have been thoroughly characterized in free
fermion models, they remain an open question for interacting bosonic systems.
In this work, we present a precise definition of quantum phases for
non-Hermitian systems and propose a new family of phases referred to as
composite quantum phases. We demonstrate the existence of these phases in a
one-dimensional spin-$1$ system and show their robustness against perturbations
through numerical simulations. Furthermore, we investigate the phase diagram of
our model, indicating the extensive presence of these new phases in
non-Hermitian systems. Our work establishes a new framework for studying and
constructing quantum phases in non-Hermitian interacting systems, revealing
exciting possibilities beyond the single-particle picture.
