Universal corner contributions to entanglement negativity

TL;DR

This paper investigates how corners in entangling surfaces affect universal contributions to entanglement negativity in higher-dimensional CFTs, revealing complex relationships with distillable entanglement through field theory and holographic methods.

Contribution

It introduces the ratio $oldsymbol{ extit{ extchi}}$ to quantify corner effects on entanglement negativity and explores its behavior across different theories and geometries, highlighting new insights into geometry-entanglement relations.

Findings

$oldsymbol{ extit{ extchi}}$ often increases with singular regions, indicating more distillable entanglement.

Counterexamples show $oldsymbol{ extit{ extchi}}$ can decrease, suggesting complex dependencies.

In free theories, $oldsymbol{ extit{ extchi}}$ is generally larger, but varies with coupling and theory type.

Abstract

It has been realised that corners in entangling surfaces can induce new universal contributions to the entanglement entropy and R\'enyi entropy. In this paper we study universal corner contributions to entanglement negativity in three- and four-dimensional CFTs using both field theory and holographic techniques. We focus on the quantity $\chi$ defined by the ratio of the universal part of the entanglement negativity over that of the entanglement entropy, which may characterise the amount of distillable entanglement. We find that for most of the examples $\chi$ takes bigger values for singular entangling regions, which may suggest increase in distillable entanglement. However, there also exist counterexamples where distillable entanglement decreases for singular surfaces. We also explore the behaviour of $\chi$ as the coupling varies and observe that for singular entangling surfaces, the amount of distillable entanglement is mostly largest for free theories, while counterexample exists for free Dirac fermion in three dimensions. For holographic CFTs described by higher derivative gravity, $\chi$ may increase or decrease, depending on the sign of the relevant parameters. Our results may reveal a more profound connection between geometry and distillable entanglement.