Entanglement negativity in free fermions: twisted characteristic polynomial, universal bounds, and area laws

TL;DR

This paper introduces a simple formula for calculating entanglement negativity in free fermions, establishing universal bounds, area laws, and insights into entanglement dynamics in open systems.

Contribution

It provides a novel, straightforward method for computing negativity in free fermions and derives universal bounds and area laws related to fermionic entanglement.

Findings

Derived a universal bound on negativity in free fermions.

Established an area-law bound on entanglement generation in open systems.

Provided analytical insights into fermionic mixed-state entanglement.

Abstract

We present a general and simple formula for computing the entanglement negativity in free fermions. Our formula allows for deriving several universal bounds on negativity and its rate of change in dynamics. The bound on negativity directly relates the clustering property of correlations in free-fermion states to the entanglement area law, and provides the optimal condition for the area law in mixed free fermion states with long-range correlations. In addition, we establish an area-law bound on entanglement generation in open systems, analogous to previously known results for entanglement entropy in unitary dynamics. Our work provides new analytical insights into fermionic mixed-state entanglement.