Scaling of tripartite entanglement at impurity quantum phase transitions

TL;DR

This paper investigates how tripartite entanglement behaves at impurity quantum phase transitions, revealing divergence and scaling behavior that indicate a shared universality class in different Kondo models.

Contribution

It introduces and applies tripartite entanglement measures to impurity systems, demonstrating their divergence and universal scaling at quantum phase transitions.

Findings

Tripartite entanglement diverges at impurity quantum phase transitions.

Critical exponents differ for each measure but suggest a common universality class.

Tripartite entanglement measures show similar critical behavior across models.

Abstract

The emergence of a diverging length scale in many-body systems at a quantum phase transition implies that total entanglement has to reach its maximum there. In order to fully characterize this, one has to consider multipartite entanglement as, for instance, bipartite entanglement between individual particles fails to signal this effect. However, quantification of multipartite entanglement is very hard and detecting it may not be possible due to the lack of accessibility to all individual particles. For these reasons it will be more sensible to partition the system into relevant subsystems, each containing few to many spins, and study entanglement between those constituents as a coarse-grain picture of multipartite entanglement between individual particles. In impurity systems, famously exemplified by two-impurity and two-channel Kondo models, it is natural to divide the system into three parts, namely, impurities and the left and right bulks. By exploiting two tripartite entanglement measures, based on negativity, we show that at impurity quantum phase transitions the tripartite entanglement diverges and shows scaling behavior. While the critical exponents are different for each tripartite entanglement measure they both provide very similar critical exponents for the two-impurity and the two-channel Kondo models suggesting that they belong to the same universality class.