Entanglement entropy of non-Hermitian free fermions

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

Automated summary

The study investigates the entanglement properties of non-Hermitian free fermionic models with translation symmetry using the correlation matrix technique, revealing a logarithmic correction to the area law in both one-dimensional and two-dimensional systems. In particular, for one-dimensional one-band systems, each Fermi point contributes exactly 1/2 to the coefficient c of the logarithmic correction. Numerical calculations and finite-size scaling analysis confirm this relation between c and Fermi point in more general one-dimensional and two-dimensional cases. Additionally, the study also explores single-particle and density-density correlation functions.