Entanglement spectrum and entropy in topological non-Hermitian systems and nonunitary conformal field theory

We study entanglement properties of free-fermion systems without Hermiticity by use of correlation matrix and overlap matrix in the biorthogonal basis. We find at a critical point in the non-Hermitian Su-Schrieffer-Heeger (SSH) model with parity and time-reversal symmetry (PT symmetry) the entanglement entropy exhibits a logarithmic scaling with corresponding central charge c=-2, signaling the emergence of nonunitary conformal field theory. In addition, we demonstrate that, in the PT-symmetric SSH model and the non-Hermitian Chern insulators, the entanglement spectrum characterizes the topological properties in terms of the existence of mid-gap states.