Entanglement properties in topological non-Hermitian systems and non-unitary conformal field theories

We compute the entanglement properties in non-Hermitian systems by use of a biorthogonal basis. For the non-Hermitian Su-Schrieffer-Heeger (SSH) model with parity and time-reversal symmetry (PT-symmetry), we find the entanglement entropy scaling at the critical point has a logarithmic scaling with corresponding central charge c=-2. This critical point is the first free-fermion lattice realization of the non-unitary conformal field theory. In addition, we use the existence of the mid-gap states in the entanglement spectrum to characterize the topological properties in both the non-Hermitian SSH model and the non-hermitian Chern insulators.