Entanglement entropy on generalized Brillouin zone

The physical interpretation of entanglement entropy in non-Hermitian systems remains unclear. The authors construct here an artificial lattice by performing a Fourier transformation on the non-Bloch Hamiltonian. Interestingly, when the generalized Brillouin zone (GBZ) is circular, the authors demonstrate that the entanglement entropy on the artificial lattices is well defined (real and positive definite). For noncircular GBZ, the non-Bloch edge entanglement entropy remains real and quantized, serving as a reliable topological indicator. The non-Bloch entanglement entropy opens new possibilities for studying many-body non-Hermitian physics.