Entanglement Entropy of Non-Hermitian Free Fermions

TL;DR

This paper investigates the entanglement entropy in non-Hermitian free fermion models, revealing a universal logarithmic correction linked to Fermi points, supported by analytical and numerical methods.

Contribution

It provides a rigorous proof of the relation between Fermi points and entanglement entropy correction in non-Hermitian free fermions, extending to higher dimensions.

Findings

Logarithmic correction to the area law in entanglement entropy.

Each Fermi point contributes exactly 1/2 to the correction coefficient.

Numerical verification of the Fermi point relation in 1D and 2D systems.

Abstract

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.