Many-Body Non-Hermitian Physics in the Generalized Brillouin Zone

The breakdown of conventional bulk-boundary correspondence (BBC) in non-Hermitian system can be resolved by the generalized Brillouin zone (GBZ) theory. However, extending the GBZ theory to interacting many-body systems remains an open problem. Here, we consider an interacting non-Hermitian model characterized by a circular GBZ. We show that, based on a GBZ transformation, a quasi-reciprocal many-body Hamiltonian can be constructed which, under periodic boundary conditions (PBC), captures the physics of the original non-Hermitian model under open boundary conditions (OBC). Using exact diagonalization (ED), we determine the phase diagram for the quasi-reciprocal many-body Hamiltonian by computing the Zak phase and the structure factor of the charge-density-wave (CDW) phase. We further investigate the entanglement properties and find that the degeneracy of the low-lying entanglement spectrum characterizes each phase in the phase diagram. These findings demonstrate that the topological properties in interacting non-Hermitian system is encoded in the entanglement spectrum of the quasi-reciprocal model. Our work establishes a route to studying many-body non-Hermitian physics within the GBZ formalism.