Quantum entanglement and non-Hermiticity in free-fermion systems

TL;DR

This review discusses recent advances in understanding entanglement in non-Hermitian free-fermion systems, highlighting how entanglement measures reveal unique properties and topological features of these quantum systems.

Contribution

It provides a comprehensive overview of how entanglement concepts are extended to non-Hermitian systems and demonstrates their utility in characterizing non-Hermitian physics.

Findings

Entanglement entropy remains a key diagnostic for non-Hermitian systems.

Entanglement spectrum reflects topological features of non-Hermitian systems.

Unique entanglement behaviors are identified in non-Hermitian free-fermion models.

Abstract

This topical review article reports rapid progress on the generalization and application of entanglement in non-Hermitian free-fermion quantum systems. We begin by examining the realization of non-Hermitian quantum systems through the Lindblad master equation, alongside a review of typical non-Hermitian free-fermion systems that exhibit unique features. A pedagogical discussion is provided on the relationship between entanglement quantities and the correlation matrix in Hermitian systems. Building on this foundation, we focus on how entanglement concepts are extended to non-Hermitian systems from their Hermitian free-fermion counterparts, with a review of the general properties that emerge. Finally, we highlight various concrete studies, demonstrating that entanglement entropy remains a powerful diagnostic tool for characterizing non-Hermitian physics. The entanglement spectrum also reflects the topological characteristics of non-Hermitian topological systems, while unique non-Hermitian entanglement behaviors are also discussed. The review is concluded with several future directions. Through this review, we hope to provide a useful guide for researchers who are interested in entanglement in non-Hermitian quantum systems.