Anyon condensation, topological quantum information scrambling, and Andreev-like reflection of non-Abelian anyons in quantum Hall interfaces

TL;DR

This paper explores how anyon condensation at quantum Hall interfaces facilitates topological quantum information scrambling, with implications for non-Abelian anyon behavior and potential Andreev-like reflections.

Contribution

It demonstrates the full gapping of the interface between Abelian and non-Abelian quantum Hall states and links this to the mechanism of information scrambling and anyon transmutation.

Findings

Interface can be fully gapped, enabling information transmutation.

Local Abelian anyon information becomes topologically stored in non-Abelian anyons.

Discussion of possible Andreev-like reflection phenomena in gapped interfaces.

Abstract

Quantum information scrambling is the spread of local information into correlation throughout the entire quantum many-body system. This concept has become a central topic in different contexts. In this work, we restate the connection between anyon condensation and topological quantum information scrambling in quantum Hall interfaces. We consider the interface between the Abelian Halperin-330 state and the non-Abelian Read-Rezayi state. We verify explicitly that the interface can be fully gapped. This allows the transmutation of local pseudospin information carried by an Abelian anyon into topological information stored entirely by the anyons in the non-Abelian quantum Hall liquid, with no scrambled information stored at the interface. In combination with our previous work [K. K. W. Ma and K. Yang, Phys. Rev. B 105, 045306 (2022)], our results demonstrate the dependence of the scrambling mechanism on the gapfulness of the interface. Possible Andreev-like reflection of non-Abelian anyons in the fully gapped interface is also discussed.