Long-range entangled zero-mode state in a non-Hermitian lattice

In contrast to a Hermitian system, in which zero modes are usually degenerate and localized edge state in the thermodynamic limit, the zero mode of a finite non-Hermitian system can be a single nontrivial long-range entangled state at the exceptional point (EP). In this work, we demonstrate this feature with a concrete example based on exact solutions. Numerical simulations show that the entangled state can be generated through the dynamic process with a high fidelity.