Composite quantum phases in non-Hermitian systems

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 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 phases in non-Hermitian systems. Our work establishes an alternate framework for studying and constructing quantum phases in non-Hermitian interacting systems, revealing exciting possibilities beyond the single-particle picture.