Review of Entanglement Entropy in Non-Hermitian Quantum Many-Body Systems: From Area Laws to Exceptional Criticality

Abstract

Entanglement entropy serves as a fundamental diagnostic for quantum many-body correlations, distinguishing quantum entanglement from classical stochastic fluctuations. This review systematically explores the scaling behaviors of entanglement entropy, beginning with the foundational area law in Hermitian systems and progressing to the exotic regimes of non-Hermitian physics. We focus on the mathematical apparatus of the Fisher-Hartwig theorem in fermionic chains, the biorthogonal formalism in non-unitary systems, and the emergence of negative entanglement entropy driven by exceptional boundary states and non-unitary conformal field theories.