Entanglement entropy of non-Hermitian free fermions

We study the entanglement properties of non-Hermitian free fermionic models with translation symmetry using correlation matrix technique. Our results show that entropy has a logarithmic correction to area law in both one-dimensional and two-dimensional systems. For any one-band system, we prove each Fermi point system contributes exactly 1/2 coefficient c correction. Moreover, this relation between is verified for more general cases by numerical calculations finite-size scaling analysis. In addition, also single-particle density-density functions.