Many-body edge burst in steady states

The interplay between the non-Hermitian skin effect and the imaginary gap of lossy lattices results in the edge burst, a boundary-induced dynamical phenomenon that an exceptionally large portion of particle loss occurs at the edge. Here, we find that such an intriguing non-Hermitian dynamical phenomenon can be exactly mapped into the steady-state density distribution of a corresponding open quantum system. Consequently, the bulk-edge scaling relation of loss probability in edge burst also maps to that of steady-state density. Moreover, we apply the positive-P representation to dissipative many-body systems with two-body loss and reveal the validity of scaling relation for steady-state correlation functions. These results provide a unique perspective of the interaction-induced many-body non-Hermitian skin effect. Our predictions are testable in state-of-the-art experimental platforms.